{ "cells": [ { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "# TRIQS Green's functions\n", "\n", "It is now time to start using some of the tools provided by TRIQS.\n", "\n", "Much of the functionality in TRIQS, while implemented in C++ for optimal performance, is exposed\n", "through a Python interface to make it easier to use. From a practical point of view this means\n", "that you can think of TRIQS as a python library, just like numpy or matplotlib.\n", "\n", "One of the central objects of a many-body calculation is a Green's function.\n", "Green's functions in TRIQS are functions defined on a mesh $\\cal{M}$ of points that hold values in some domain $\\cal{D}$, for example $\\mathbb{C}^{2\\times2}$\n", "\n", "$$\n", "G: \\cal{M} \\rightarrow \\cal{D}\n", "$$\n", "\n", "A few common Green's function meshes in TRIQS include:\n", "\n", "- `MeshReFreq` - Real-frequencies equally spaced in $[\\omega_{min},\\omega_{max}]$\n", "- `MeshImFreq` - Matsubara Frequencies\n", "- `MeshImTime` - Imaginary time points equally spaced in $[0,\\beta]$\n", "- `MeshReTime` - Real-time points (not covered in this tutorial)\n", "\n", "Let's see how we can **construct a Mesh and print its values**." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\u001b[0;31mInit signature:\u001b[0m \u001b[0mMeshImTime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m/\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mDocstring:\u001b[0m \n", "Mesh of imaginary times\n", "\n", "Mesh-points are evenly distributed in the interval [0,beta]\n", "including points at both edges.\n", "\n", "Parameters\n", "----------\n", "beta : float\n", " Inverse temperature\n", "statistic : str\n", " Statistic, 'Fermion' or 'Boson'\n", "n_tau : int\n", " Number of mesh-points\n", "\u001b[0;31mFile:\u001b[0m ~/opt/triqs/lib/python3.11/site-packages/triqs/gf/meshes.cpython-311-darwin.so\n", "\u001b[0;31mType:\u001b[0m type\n", "\u001b[0;31mSubclasses:\u001b[0m " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Import the Mesh type we want to use\n", "from triqs.gf import MeshImTime\n", "\n", "# The documentation tells us which parameters we need to pass for the mesh construction\n", "?MeshImTime" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.448048Z", "iopub.status.busy": "2023-08-28T15:03:58.447950Z", "iopub.status.idle": "2023-08-28T15:03:58.449936Z", "shell.execute_reply": "2023-08-28T15:03:58.449731Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0\n", "0.5\n", "1.0\n", "1.5\n", "2.0\n", "2.5\n", "3.0\n", "3.5\n", "4.0\n", "4.5\n", "5.0\n" ] } ], "source": [ "# Provide the inverse temperature, Statistic, and number of points\n", "tau_mesh = MeshImTime(beta=5, S='Fermion', n_tau=11)\n", "\n", "# We can loop and print the mesh-point values\n", "for tau in tau_mesh:\n", " print(tau.value)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now **create and initialize a Green's function for a single atomic level** with energy $\\epsilon$ in the grand-canonical ensemble with inverse temperature $\\beta$\n", "\n", "$$\n", "G[\\tau] = -\\langle\\cal{T}c(\\tau) c^\\dagger\\rangle = -\\frac{e^{-\\tau \\epsilon}}{1+e^{-\\beta \\epsilon}}\n", "= -\\frac{e^{\\left(\\beta \\Theta(-\\epsilon) -\\tau\\right) \\epsilon}}{1+e^{-\\beta |\\epsilon|}}$$\n", "\n", "In practice we use the second expression, as it avoids diverging exponentials for large values of $\\beta$.\n", "We first have a look at the documentation for `Gf`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\u001b[0;31mInit signature:\u001b[0m \u001b[0mGf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mDocstring:\u001b[0m \n", "TRIQS Greens function container class\n", "\n", "Parameters\n", "----------\n", "\n", "mesh: Types defined in triqs.gf beginning with 'Mesh'\n", " The mesh on which the Green function is defined.\n", "\n", "data: numpy.array, optional\n", " The data of the Greens function.\n", " Must be of dimension ``mesh.rank + target_rank``.\n", "\n", "target_shape: list of int, optional\n", " Shape of the target space.\n", "\n", "is_real: bool\n", " Is the Greens function real valued?\n", " If true, and target_shape is set, the data will be real.\n", " Mutually exclusive with argument ``data``.\n", "\n", "name: str \n", " The name of the Greens function for plotting.\n", "\n", "Notes\n", "-----\n", "\n", "One of ``target_shape`` or ``data`` must be set, and the other must be `None`.\n", "\u001b[0;31mFile:\u001b[0m ~/opt/triqs/lib/python3.11/site-packages/triqs/gf/gf.py\n", "\u001b[0;31mType:\u001b[0m AddMethod\n", "\u001b[0;31mSubclasses:\u001b[0m GfReFreq, GfImFreq, GfImTime, GfReTime, GfLegendre" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from triqs.gf import Gf\n", "?Gf" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.469637Z", "iopub.status.busy": "2023-08-28T15:03:58.469541Z", "iopub.status.idle": "2023-08-28T15:03:58.471763Z", "shell.execute_reply": "2023-08-28T15:03:58.471565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Greens Function with mesh Imaginary Time Mesh with beta = 5, statistic = Fermion, n_tau = 11 and target_shape (): \n", "\n", "-0.119\n", "-0.146\n", "-0.178\n", "-0.217\n", "-0.265\n", "-0.324\n", "-0.396\n", "-0.483\n", "-0.590\n", "-0.721\n", "-0.881\n" ] } ], "source": [ "# Create scalar-valued imaginary-time Green's function\n", "G = Gf(mesh=tau_mesh, target_shape=[], is_real=True)\n", "\n", "# Print the Green's function description\n", "print(G)\n", "\n", "# Loop initialization\n", "eps = -0.4\n", "beta = G.mesh.beta\n", "from math import exp\n", "for tau in G.mesh:\n", " G[tau] = -exp((beta*(eps<0) - tau.value) * eps) / (1. + exp(-beta * abs(eps)))\n", " print(\"{:.3f}\".format(G[tau]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to **plot this Green's function** we can use the matplotlib interface defined in TRIQS.\n", "Note that the function to plot Green's function is `oplot` and not just `plot` like in matplotlib." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.473018Z", "iopub.status.busy": "2023-08-28T15:03:58.472934Z", "iopub.status.idle": "2023-08-28T15:03:58.736480Z", "shell.execute_reply": "2023-08-28T15:03:58.736227Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from triqs.plot.mpl_interface import oplot,plt\n", "\n", "# Make plots show up directly in the notebook:\n", "%matplotlib inline\n", "\n", "# Make all figures slightly bigger\n", "import matplotlib as mpl\n", "mpl.rcParams['figure.dpi']=100\n", "\n", "# Additional arguments like 'linewidth' are passed on to matplotlib\n", "oplot(G, '-', name='G', linewidth=2)" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Matrix-Valued Green's functions\n", "\n", "In most realistic problems we have to treat more than just a single orbital\n", "\n", "$$\n", "G_{ij}[\\tau] = -\\langle\\cal{T}c_i(\\tau) c_j^\\dagger\\rangle\n", "$$\n", "\n", "For this purpose, TRIQS provides Green's functions that have a Matrix structure. Let's see how you can create and use them" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.737885Z", "iopub.status.busy": "2023-08-28T15:03:58.737792Z", "iopub.status.idle": "2023-08-28T15:03:58.740099Z", "shell.execute_reply": "2023-08-28T15:03:58.739889Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (2, 2): " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# A uniform real-frequency mesh on a given interval\n", "from triqs.gf import MeshReFreq\n", "w_mesh = MeshReFreq(window=(-4,4), n_w=1000)\n", "\n", "# Gf with 2x2 Matrix structure holding complex values\n", "G = Gf(mesh=w_mesh, target_shape=[2,2])\n", "G # <- Same as print(repr(G))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.741226Z", "iopub.status.busy": "2023-08-28T15:03:58.741159Z", "iopub.status.idle": "2023-08-28T15:03:58.742729Z", "shell.execute_reply": "2023-08-28T15:03:58.742529Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.+0.j 0.+0.j]\n", " [0.+0.j 0.+0.j]]\n" ] } ], "source": [ "# Accessing a specific mesh point gives us a matrix\n", "from triqs.gf import Idx # Use Idx to access Gf at specific Index\n", "print(G[Idx(0)])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.743789Z", "iopub.status.busy": "2023-08-28T15:03:58.743721Z", "iopub.status.idle": "2023-08-28T15:03:58.745579Z", "shell.execute_reply": "2023-08-28T15:03:58.745351Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (): " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# By Fixing the orbital indices we obtain a Green's function that is no longer matrix but complex-valued\n", "G[0,0]" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Block Green's functions\n", "\n", "In many realistic problems we know a priori that (due to e.g. symmetries or conserved quantum numbers) certain components of the Green's function will vanish.\n", "In other words, the Green's functions has an additional *block structure*.\n", "\n", "$$\n", "\\hat{G} =\n", "\\begin{pmatrix}\n", "\\hat{g}^0 & 0 & \\cdots & \\cdots \\\\\n", "0 & \\hat{g}^1 & 0 & \\cdots \\\\\n", "\\cdots & 0 & \\hat{g}^2 & 0 \\\\\n", "\\cdots & \\cdots & \\cdots & \\cdots\n", "\\end{pmatrix}\n", "$$\n", "\n", "Here the $\\hat{g}^i$ are Green's functions with non-zero elements $g^i_{ab}$. In principle they can have\n", "different dimensions.\n", "\n", "For example, you can imagine a system of 5 $d$-orbitals that are split by a\n", "crystal field into 3 $t_{2g}$-orbitals and 2 $e_g$-orbitals. For symmetry reasons, you can have a\n", "situation where these orbitals do not talk to each other. In that case, the complete Green's function\n", "would have two blocks, one of size 2x2 corresponding to the $e_g$ orbitals and one of size 3x3 corresponding for the $t_{2g}$ orbitals. \n", "\n", "$$\n", "\\hat{G} =\n", "\\begin{pmatrix}\n", "\\hat{g}^{e_g} & 0 \\\\\n", "0 & \\hat{g}^{t_{2g}} \\\\\n", "\\end{pmatrix}=\n", "\\begin{pmatrix}\n", "\\begin{pmatrix}\n", "g^{e_g}_{00} & g^{e_g}_{01} \\\\\n", "g^{e_g}_{10} & g^{e_g}_{11}\n", "\\end{pmatrix} & 0 \\\\\n", "0 & \\begin{pmatrix}\n", "g^{t_{2g}}_{00} & g^{t_{2g}}_{01} & g^{t_{2g}}_{02} \\\\\n", "g^{t_{2g}}_{10} & g^{t_{2g}}_{11} & g^{t_{2g}}_{12} \\\\\n", "g^{t_{2g}}_{20} & g^{t_{2g}}_{21} & g^{t_{2g}}_{22} \\\\\n", "\\end{pmatrix}\n", "\\end{pmatrix}\n", "$$\n", "\n", "Let us now consider a more concrete example for the case outlined above:\n", "$$\n", "\\hat{G} =\n", "\\begin{pmatrix}\n", "\\begin{pmatrix}\n", "\\omega & V_1 \\\\\n", "V_1 & \\omega\n", "\\end{pmatrix}^{-1} & 0 \\\\\n", "0 & \\begin{pmatrix}\n", "\\omega - \\epsilon_2 & 0 & V_2 \\\\\n", "0 & \\omega - \\epsilon_2 & 0 \\\\\n", "V_2 & 0 & \\omega - \\epsilon_2\n", "\\end{pmatrix}^{-1}\n", "\\end{pmatrix}\n", "$$\n", "\n", "The associated type in TRIQS is called `BlockGf`. Let us have a first look at it's documentation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\u001b[0;31mInit signature:\u001b[0m \u001b[0mBlockGf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mDocstring:\u001b[0m Generic Green's Function by Block.\n", "\u001b[0;31mInit docstring:\u001b[0m\n", "* There are several possible constructors, which accept only keyword arguments.\n", "\n", " * BlockGf(block_list = list of blocks, name_list = list of names, make_copies = False)\n", "\n", " * ``block_list``: list of blocks of Green's functions.\n", " * ``name_list``: list of the names of the blocks, e.g. [\"up\",\"down\"]. Default to [\"0\", \"1\", ...]\n", " * ``make_copies``: If True, build the Green's function from a copy of the blocks (default: False).\n", "\n", " * BlockGf(mesh = mesh, gf_struct = block structure, target_rank = rank of target space)\n", "\n", " * ``mesh``: The mesh used to construct each block\n", " * ``gf_struct``: List of pairs [ (str,int), ... ] providing the block name and its linear size\n", " * ``target_rank``: The rank of the target space of each block (default: 2)\n", "\n", " * BlockGf(name_block_generator, make_copies = False)\n", "\n", " * ``name_block_generator``: a generator of (name, block)\n", " * ``make_copies``: If True, build the Green's function from a copy of the blocks (default: False).\n", "\n", " \n", "\u001b[0;31mFile:\u001b[0m ~/opt/triqs/lib/python3.11/site-packages/triqs/gf/block_gf.py\n", "\u001b[0;31mType:\u001b[0m type\n", "\u001b[0;31mSubclasses:\u001b[0m " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from triqs.gf import BlockGf\n", "?BlockGf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will in the following consider the first two options for the construction listed in the documentation.\n", "\n", "The first way is to simply define the two Green's function blocks separately, and to then pass these blocks, together with their names:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.749683Z", "iopub.status.busy": "2023-08-28T15:03:58.749620Z", "iopub.status.idle": "2023-08-28T15:03:58.751494Z", "shell.execute_reply": "2023-08-28T15:03:58.751285Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Green Function G composed of 2 blocks: \n", " Greens Function G_eg with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (2, 2): \n", " \n", " Greens Function G_t2g with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (3, 3): \n", " \n", "\n" ] } ], "source": [ "# Construct individual blocks\n", "g_eg = Gf(mesh=w_mesh, target_shape=[2,2])\n", "g_t2g = Gf(mesh=w_mesh, target_shape=[3,3])\n", "\n", "# Combine blocks into a BlockGf\n", "G = BlockGf(name_list=['eg', 't2g'], block_list=[g_eg, g_t2g])\n", "print(G)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then access individual blocks simply by using their name" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.752651Z", "iopub.status.busy": "2023-08-28T15:03:58.752587Z", "iopub.status.idle": "2023-08-28T15:03:58.754315Z", "shell.execute_reply": "2023-08-28T15:03:58.754118Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function G_eg with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (2, 2): " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G['eg']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For cases where all blocks have a square-matrix `target_shape` we can alternatively pass a list of pairs of block-names and linear matrix sizes." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.755483Z", "iopub.status.busy": "2023-08-28T15:03:58.755408Z", "iopub.status.idle": "2023-08-28T15:03:58.757105Z", "shell.execute_reply": "2023-08-28T15:03:58.756889Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Green Function G composed of 2 blocks: \n", " Greens Function G_eg with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (2, 2): \n", " \n", " Greens Function G_t2g with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (3, 3): \n", " \n", "\n" ] } ], "source": [ "# List of Block-names and their linear matrix size\n", "gf_struct = [('eg',2), ('t2g',3)]\n", "\n", "G = BlockGf(mesh=w_mesh, gf_struct=gf_struct)\n", "print(G)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now initialize the Green's function values. Instead of writing a loop over the mesh, we here make use of the the operator `<<`, which can fill the Green's function with simple expressions containing the `Omega` descriptor. Here `Omega` is replaced by the values of the mesh." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.758429Z", "iopub.status.busy": "2023-08-28T15:03:58.758362Z", "iopub.status.idle": "2023-08-28T15:03:58.766758Z", "shell.execute_reply": "2023-08-28T15:03:58.766560Z" } }, "outputs": [], "source": [ "from triqs.gf import Omega\n", "\n", "V1 = 0.1\n", "V2 = 0.2\n", "eps_t2g = -2.0\n", "\n", "# The e_g part\n", "G['eg'][0,0] << Omega\n", "G['eg'][0,1] << V1\n", "G['eg'][1,0] << V1\n", "G['eg'][1,1] << Omega\n", "\n", "# Perform an in-place Matrix inversion\n", "G['eg'].invert()\n", "\n", "# The t_2g part\n", "G['t2g'][0,0] << Omega - eps_t2g\n", "G['t2g'][1,1] << Omega - eps_t2g\n", "G['t2g'][2,2] << Omega - eps_t2g\n", "G['t2g'][0,2] << V2\n", "G['t2g'][2,0] << V2\n", "G['t2g'].invert()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using the Green's function object, it is often convenient to **iterate over all the blocks** of a `BlockGf`. We can do this with the following construct" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.768008Z", "iopub.status.busy": "2023-08-28T15:03:58.767932Z", "iopub.status.idle": "2023-08-28T15:03:58.769621Z", "shell.execute_reply": "2023-08-28T15:03:58.769354Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is the block called eg\n", "The associated Green's function is Greens Function G_eg with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (2, 2): \n", "\n", "This is the block called t2g\n", "The associated Green's function is Greens Function G_t2g with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (3, 3): \n", "\n" ] } ], "source": [ "# Loop over the blocks\n", "for name, g in G:\n", " print(\"This is the block called\", name)\n", " print(\"The associated Green's function is\", g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Additional Initialization Descriptors\n", "\n", "In the following we will introduce a few additional means of initializing Green's functions using `<<`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Flat density of states\n", "Consider the problem of a single impurity level embedded in a flat conduction bath $\\Gamma$ of electrons.\n", "$$\n", "g^\\mathrm{imp} (\\omega) = \\frac{1}{\\omega - \\epsilon_d - V^2 \\Gamma(\\omega)}\n", "$$\n", "\n", "In the equation above $\\epsilon_d$ is the energy of the level and $\\Gamma$ is the Green's function of\n", "a flat conduction bath\n", "\n", "$$\n", "\\Gamma(\\omega) = \\int_{-D}^{D}\\frac{1}{\\omega-\\epsilon + i\\eta}\\frac{d\\epsilon}{2D}\n", "$$\n", "\n", "Here $D$ denotes the half-bandwidth.\n", "Let's see how to define and then plot this Green's function by using `inverse` and the `Flat` descriptor." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.770800Z", "iopub.status.busy": "2023-08-28T15:03:58.770738Z", "iopub.status.idle": "2023-08-28T15:03:58.775847Z", "shell.execute_reply": "2023-08-28T15:03:58.775632Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function with mesh Real Freq Mesh with w_min = -4, w_max = 4, n_w = 1000 and target_shape (): " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps_d = 1.0 # Energy\n", "V = 0.2 # Bath Hybridization\n", "D = 1.5 # Half bandwidth\n", "\n", "G = Gf(mesh=w_mesh, target_shape=[])\n", "\n", "from triqs.gf import Omega, Flat, inverse\n", "G << inverse(Omega - eps_d - V**2 * Flat(D))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the predefined function `Flat` for a flat conduction bath $\\Gamma(\\omega)$.\n", "Let's plot the impurity Green's function. Note that default, both the real and imaginary parts are plotted." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.777048Z", "iopub.status.busy": "2023-08-28T15:03:58.776989Z", "iopub.status.idle": "2023-08-28T15:03:58.844916Z", "shell.execute_reply": "2023-08-28T15:03:58.844688Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "oplot(G, '-', linewidth=2, name=\"G\") " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the spectral function, which is defined as\n", "\n", "$$ \\rho(\\omega) = -\\frac{1}{\\pi} \\, \\textbf{Im} \\, G $$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.846426Z", "iopub.status.busy": "2023-08-28T15:03:58.846353Z", "iopub.status.idle": "2023-08-28T15:03:58.912041Z", "shell.execute_reply": "2023-08-28T15:03:58.911783Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import pi\n", "oplot(-G.imag/pi, linewidth=2, name=r\"$\\rho$\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected the spectral function is peaked at $\\epsilon_d$ and shows a jump in spectral weight at $D$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Semi-circular density of states\n", "\n", "Another predefined Green's function is the one corresponding to a semi-circular spectral function. This one will be useful in the DMFT Tutorials later on." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.913468Z", "iopub.status.busy": "2023-08-28T15:03:58.913402Z", "iopub.status.idle": "2023-08-28T15:03:58.980774Z", "shell.execute_reply": "2023-08-28T15:03:58.980547Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "D = 1.0 # Half bandwidth\n", "\n", "G = Gf(mesh=w_mesh, target_shape=[])\n", "\n", "from triqs.gf import SemiCircular\n", "G << SemiCircular(D)\n", "\n", "oplot(-G.imag/pi, name=r\"$\\rho$\") " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Imaginary-frequency Green's functions\n", "-------------------------------------\n", "\n", "These are Green's function defined on the Matsubara axis. The fermionic Matsubara frequencies\n", "are defined by\n", "\n", "$$\\omega_n = \\frac{(2n+1)\\pi}{\\beta}$$\n", "\n", "where $\\beta = 1/T$ is the inverse temperature. These Green's functions are important because\n", "most Monte Carlo algorithms yield results on the Matsubara axis. Let's see how they\n", "are defined:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:58.982199Z", "iopub.status.busy": "2023-08-28T15:03:58.982129Z", "iopub.status.idle": "2023-08-28T15:03:59.075776Z", "shell.execute_reply": "2023-08-28T15:03:59.075550Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 10.0)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the imaginary-frequency mesh\n", "from triqs.gf import MeshImFreq\n", "iw_mesh = MeshImFreq(beta=5, S='Fermion', n_iw=1000)\n", "\n", "# Create Green's function and fill it using the iOmega_n descriptor\n", "G = Gf(mesh=iw_mesh, target_shape=[])\n", "from triqs.gf import iOmega_n\n", "G << inverse(iOmega_n - 0.2)\n", "\n", "# Plot the Green's function\n", "oplot(G, '-o', name='G')\n", "plt.xlim(0,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Arithmetic Operations\n", "\n", "Green's functions can be added, multiplied by numbers, etc. The way this is done is quite natural." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.077138Z", "iopub.status.busy": "2023-08-28T15:03:59.077067Z", "iopub.status.idle": "2023-08-28T15:03:59.159460Z", "shell.execute_reply": "2023-08-28T15:03:59.159239Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 10.0)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "oplot(G, \"-o\", name='G')\n", "oplot(G+G, \"-o\", name='G+G')\n", "oplot(3*G+2, \"-o\", name='3*G+2')\n", "plt.xlim(0,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Obtaining the density\n", "\n", "You can obtain the density for Green's functions with a `MeshReFreq` and `MeshImFreq` using the `density` method" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.160726Z", "iopub.status.busy": "2023-08-28T15:03:59.160658Z", "iopub.status.idle": "2023-08-28T15:03:59.166773Z", "shell.execute_reply": "2023-08-28T15:03:59.166565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Density = (0.26894142138025784+1.816357384858482e-15j)\n" ] } ], "source": [ "G = Gf(mesh=iw_mesh, target_shape=[])\n", "G << inverse(iOmega_n - 0.2)\n", "print(\"Density =\", G.density())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do not worry about the imaginary component as the machine precision is on the order of $10^{-15}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fourier transforms\n", "\n", "TRIQS allows you to easily Fourier transform Green's functions from imaginary-time to imaginary-frequency." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.168089Z", "iopub.status.busy": "2023-08-28T15:03:59.168024Z", "iopub.status.idle": "2023-08-28T15:03:59.234020Z", "shell.execute_reply": "2023-08-28T15:03:59.233784Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A Green's function in frequency set to semi-circular\n", "Giw = Gf(mesh=iw_mesh, target_shape=[])\n", "Giw << SemiCircular(1.0)\n", "\n", "# A Green's function in time set by inverse Fourier transform\n", "from triqs.gf import make_gf_from_fourier\n", "Gtau = make_gf_from_fourier(Giw)\n", "oplot(Gtau, name='G')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also go the other way. Let's check that it gives back the original result." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.235308Z", "iopub.status.busy": "2023-08-28T15:03:59.235237Z", "iopub.status.idle": "2023-08-28T15:03:59.305266Z", "shell.execute_reply": "2023-08-28T15:03:59.305066Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 5.0)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Giw_2 = make_gf_from_fourier(Gtau)\n", "oplot(Giw, 'o')\n", "oplot(Giw_2, 'x')\n", "plt.xlim(0,5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example above `make_gf_from_fourier` will construct a new Green's function object.\n", "This uses the `statistic` information of `MeshImTime` to decide wether to use bosonic or fermionic Matsubara frequencies.\n", "If we want to instead use an existing Green's function we can use the `Fourier` descriptor" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.306527Z", "iopub.status.busy": "2023-08-28T15:03:59.306454Z", "iopub.status.idle": "2023-08-28T15:03:59.308760Z", "shell.execute_reply": "2023-08-28T15:03:59.308568Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function with mesh Imaginary Time Mesh with beta = 5, statistic = Fermion, n_tau = 6001 and target_shape (): " ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from triqs.gf import Fourier\n", "Gtau << Fourier(Giw)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compact meshes for imaginary time / frequency: DLR Green's function\n", "\n", "When representing Green's functions at low temperatures the regular meshes `MeshImFreq` and `MeshImTime` may easily require several thousand of points to store the relevant information. This is often problematic when storing or initializing lattice Green's functions\n", "with a momentum and orbital dependence.\n", "\n", "For this purpose TRIQS provides mesh types on the Matsubara / imaginary time axis that are much more compact,\n", "based on the Discrete Lehman Representation (DLR), for a detailed introduction see [Kaye et al., PRB105, 2022](https://doi.org/10.1103/PhysRevB.105.235115).\n", "\n", "The DLR of an imaginary time Green's function is given by an expansion of the form\n", "\n", "$$ G(\\tau) \\approx \\sum_{l=1}^r K(\\tau, \\omega_l) \\, \\widehat{g}_l $$\n", "\n", "where $K(\\tau,\\omega) = -\\frac{e^{-\\tau \\omega}}{1+e^{-\\beta \\omega}}$ is the analytic continuation kernel appearing in the spectral Lehmann representation\n", "\n", "$$ G(\\tau) = \\int_{-\\infty}^\\infty d\\omega \\, K(\\tau, \\omega) \\rho(\\omega) $$\n", "\n", "relating $G$ to its spectral density $\\rho$. \n", "\n", "The DLR frequencies $\\omega_l$ are obtained by a numerical scheme that is independent of the specific Green's function $G$. They depend only on the desired accuracy $\\epsilon$ of the DLR expansion, and a dimensionless cutoff parameter $\\Lambda = \\beta \\omega_{max}$ characterized by the assumption that $\\rho(\\omega) = 0$ outside of the interval $[-\\omega_{max}, \\omega_{max}]$. The DLR basis is one of the most compact representations of Matsubara Green's functions and the basis size scales only logarithmically with $\\beta$.\n", "\n", "To get started we first create a Matsubara Green's function with a SemiCircular density of states function at a low temperature of $\\beta=100$. For the imaginary part of G to decay to zero we have to use as many as `~1500` Matsubara frequencies." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.309975Z", "iopub.status.busy": "2023-08-28T15:03:59.309904Z", "iopub.status.idle": "2023-08-28T15:03:59.316075Z", "shell.execute_reply": "2023-08-28T15:03:59.315877Z" } }, "outputs": [ { "data": { "text/plain": [ "Greens Function with mesh Imaginary Freq Mesh with beta = 100, statistic = Fermion, n_iw = 1500, positive_only = false and target_shape (): " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iw_mesh = MeshImFreq(beta=100, S='Fermion', n_iw=1500)\n", "Giw = Gf(mesh=iw_mesh, target_shape=[])\n", "Giw << SemiCircular(1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now construct a DLR Matsubara Green's function. Similar to the MeshImFreq we have to provide $\\beta$ and the particle statistics. Additionally we set the maximal spectral width of the Greens function `w_max` (half spectral width), plus the precision we want to achieve with the DLR basis:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.317369Z", "iopub.status.busy": "2023-08-28T15:03:59.317309Z", "iopub.status.idle": "2023-08-28T15:03:59.329773Z", "shell.execute_reply": "2023-08-28T15:03:59.329565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DLR imfreq mesh of size 43 with beta = 100, statistic = Fermion, w_max = 1.2, eps = 1e-15\n" ] } ], "source": [ "# import DLR mesh\n", "from triqs.gf.meshes import MeshDLRImFreq\n", "\n", "dlr_iw_mesh = MeshDLRImFreq(beta=100, statistic='Fermion', w_max=1.2, eps=1e-15)\n", "# the Gf is constructed then the same way\n", "Giw_dlr = Gf(mesh= dlr_iw_mesh, target_shape=[])\n", "\n", "print(dlr_iw_mesh)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By printing the mesh we see that its size is `43` which is substantially smaller than `1500`.\n", "We can initialize the DLR Matsubara Green's function using the same syntax as before" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.330987Z", "iopub.status.busy": "2023-08-28T15:03:59.330922Z", "iopub.status.idle": "2023-08-28T15:03:59.332474Z", "shell.execute_reply": "2023-08-28T15:03:59.332265Z" } }, "outputs": [], "source": [ "Giw_dlr << SemiCircular(1.0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now plot both Green's functions:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.333685Z", "iopub.status.busy": "2023-08-28T15:03:59.333624Z", "iopub.status.idle": "2023-08-28T15:03:59.421940Z", "shell.execute_reply": "2023-08-28T15:03:59.421724Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,figsize=(12,5))\n", "oplot(Giw, \"-\", name='G')\n", "oplot(Giw_dlr, name='G DLR')\n", "plt.xlim(-0.1,94)\n", "plt.ylim(-2,0.1)\n", "plt.legend(loc='lower right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The DLR mesh Matsubara nodes are quite sparse but as we will see below the data is sufficient to reconstruct the full Matsubara mesh up to the precision specified. \n", "\n", "Next we create the DLR coefficient Green's function associated with `Giw_dlr`. This form is central as it can be easily converted into a `Gf` with any of the mesh types `MeshImTime`, `MeshImFreq`, `MeshDLRImTime` and `MeshDLRImFreq`.\n", "\n", "We obtain the Green's function on the full Matsubara mesh using the function `make_gf_imfreq` to then compare it against the original `Giw`. " ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.423235Z", "iopub.status.busy": "2023-08-28T15:03:59.423169Z", "iopub.status.idle": "2023-08-28T15:03:59.559066Z", "shell.execute_reply": "2023-08-28T15:03:59.558854Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# import helper functions\n", "from triqs.gf import make_gf_dlr, make_gf_dlr_imtime, make_gf_imfreq, make_gf_imtime\n", "\n", "# create DLR coefficient Green's function\n", "G_dlr = make_gf_dlr(Giw_dlr)\n", "\n", "# Get back Green's function on the full Matsubara mesh, no Fourier transform needed\n", "Giw_from_dlr = make_gf_imfreq(G_dlr, n_iw=1500)\n", "\n", "# plot the difference between the original\n", "fig, ax = plt.subplots(1,figsize=(7,5))\n", "\n", "mesh = [iw.imag for iw in Giw.mesh.values()]\n", "ax.plot(mesh, abs((Giw_from_dlr-Giw).data))\n", "ax.semilogy()\n", "ax.set_xlim(0,94)\n", "ax.set_xlabel(r'$i\\omega_n$')\n", "ax.set_ylabel(r'$|G_{ref}-G_{DLR}|$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The given accuracy `eps=1e-15` is reached over the full Matsubara mesh!\n", "\n", "The coefficient DLR mesh Gf can be evaluated on any given tau point by passing the Gf a float:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.560424Z", "iopub.status.busy": "2023-08-28T15:03:59.560351Z", "iopub.status.idle": "2023-08-28T15:03:59.562264Z", "shell.execute_reply": "2023-08-28T15:03:59.562074Z" } }, "outputs": [ { "data": { "text/plain": [ "(-0.31556737050747535-9.638049093627782e-17j)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G_dlr(1.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or on the Matsubara axis by passing a Matsubara mesh point:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.563495Z", "iopub.status.busy": "2023-08-28T15:03:59.563435Z", "iopub.status.idle": "2023-08-28T15:03:59.565227Z", "shell.execute_reply": "2023-08-28T15:03:59.565032Z" } }, "outputs": [ { "data": { "text/plain": [ "(6.83481049534862e-16-1.9381548639656863j)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G_dlr(iw_mesh(0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we can also construct an imaginary time Green's functions, using `make_gf_dlr_imtime` on the compact mesh, and using `make_gf_imtime` on arbirarily dense $\\tau$ meshes by passing the parameter `n_tau`:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.566414Z", "iopub.status.busy": "2023-08-28T15:03:59.566345Z", "iopub.status.idle": "2023-08-28T15:03:59.631892Z", "shell.execute_reply": "2023-08-28T15:03:59.631687Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gtau_dlr = make_gf_dlr_imtime(G_dlr)\n", "Gtau = make_gf_imtime(G_dlr, n_tau=5001)\n", "\n", "oplot(Gtau_dlr.real, name='G DLR')\n", "oplot(Gtau.real, name='G')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pade analytical continuation\n", "\n", "The Fourier transforms allow to go from time to frequency. A much more delicate thing is to do the so-called \"analytical continuation\". This means to start from a Matsubara-frequency Green's function and obtain the corresponding real-frequency Green's function. This can formally be done, but turns out to be a mathematically ill-conditioned problem. Even small amounts of noise in the Matsubara-frequency data will make the continuation to the real axis very unstable.\n", "\n", "One of the ways to do perform analytical continuation is to use [Pade approximants](https://en.wikipedia.org/wiki/Padé_approximant#Definition). TRIQS can do that for you in the following way:\n", "\n", "*Note:* Pade is currently implemented only for Green's functions with a Matrix structure" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.633117Z", "iopub.status.busy": "2023-08-28T15:03:59.633053Z", "iopub.status.idle": "2023-08-28T15:03:59.710725Z", "shell.execute_reply": "2023-08-28T15:03:59.710512Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The Matsubara Green's function to be continued\n", "iw_mesh = MeshImFreq(beta=50, S='Fermion', n_iw=1000)\n", "Giw = Gf(mesh=iw_mesh, target_shape=[1,1])\n", "Giw << SemiCircular(1.0)\n", "\n", "# Construct real-frequency Green's function and initialize it using Pade approximants\n", "Gw = Gf(mesh=w_mesh, target_shape=[1,1])\n", "Gw.set_from_pade(Giw)\n", "\n", "oplot(-Gw.imag/pi, linewidth=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coarse Matsubara discretization at high temperatures will worsen the Pade result, which is why we chose a much lower temperature value for this example.\n", "\n", "You can see that the Pade continuation did a pretty good job. We will see later that noise will completely change this picture!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Define the following real-frequency Green's function, where $\\Gamma$ is the Green's function of a\n", "flat bath (width = 1), $\\epsilon_d = 0.3$ and $V=0.2$:\n", "\n", "$$\n", "G^\\mathrm{s+d} (\\omega) =\n", "\\begin{pmatrix} \\omega - \\epsilon_d & V \\\\\\\\ V & \\Gamma^{-1}\n", "\\end{pmatrix}^{-1}\n", "$$\n", "\n", "Plot the spectral function for both diagonal components of this Green's function. What\n", "do they represent physically?" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.712097Z", "iopub.status.busy": "2023-08-28T15:03:59.712026Z", "iopub.status.idle": "2023-08-28T15:03:59.783014Z", "shell.execute_reply": "2023-08-28T15:03:59.782770Z" } }, "outputs": [ { "data": { "image/png": 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KCgYWIqJWiKLo7GFxnxkEuHpcOCREFBwMLERErWiwibCL0vWmPSyODRA5JEQUHAwsREStcF80ztC0hqUxsNQ32CCKYlDbRRSJGFiIiFpR38KicU1v20XAYmMdC5HSGFiIiFrhviicqZXA0vQ4IlIGAwsRUSs89xHy/Lg0ud02s46FSHEMLERErfDYqdlLDwsLb4mUx8BCRNQK96GeZoFFxyEhomBiYCEiaoV7z4n7/kGA57os7GEhUh4DCxFRKzyGhJosHOc+zZmLxxEpj4GFiKgVHoGllYXjAPawEAUDAwsRUSvM3mpY3G5zlhCR8hhYiIha4X1aM4tuiYKJgYWIqBV1Xle6dX18ckiISHkMLERErWj/SrcMLERKY2AhImpFezY/BNjDQhQMDCxERK1o70q3rGEhUl7IBZbFixdDEATMmzdP7aYQUYRr77RmzhIiUl5IBZZt27bh3XffxaBBg9RuChFRk6X5mw4JseiWKJhCJrBUV1djxowZeP/995GUlKR2c4iIPHpYTHoW3RKpKWQCy9y5c3HDDTdg4sSJbR5rNptRWVnpcSEikpu3ISFufkgUXDq1GwAAK1aswM6dO7Ft27Z2Hb9o0SIsXLhQ4VYRUaTzulsz9xIiCirVe1iKiorw6KOP4u9//zuMRmO7nrNgwQJUVFQ4L0VFRQq3kogikXttiqHJbs3umyHWW9nDQqQ01XtYduzYgZKSEgwdOtR5n81mw8aNG/HWW2/BbDZDq22yS6rBAIPBEOymElGEcfSc6HUaaDSCx2OeQ0LsYSFSmuqB5ZprrsHu3bs97rv33ntx+eWX48knn2wWVoiIgsXc2HPSdJVbAIjSCtAIgF1kYCEKBtUDS1xcHAYMGOBxX0xMDFJSUprdT0QUTI4g0nRKMwAIggBjlBa1FhsDC1EQqF7DQkQUqlyBpeWeXsf9nCVEpDzVe1haUlBQoHYTiIicRbdNpzQ7GBsLcdnDQqQ89rAQEbVAFEVnz4lR31YPCwMLkdIYWIiIWmB2m6ps1LX8UWlwBBZOayZSHAMLEVELzF4WjXPdL32EWqx22O1iUNpFFKkYWIiIWuC+aFxLs4QAz9oWM3tZiBTFwEJE1AKPfYTa6GFpejwRyY+BhYioBfVWt52a25jW3PR4IpIfAwsRUQu8bXzY0v1ci4VIWQwsREQtcB/iMbRWw8IhIaKgYWAhImqBR9FtKwvHGdzur2NgIVIUAwsRUQvM7Si6Nem5YzNRsDCwEBG1wL0mxdSeac2sYSFSFAMLEVELOK2ZKLQwsBARtaB9gYXTmomChYGFiKgFdR7TmtszS4hDQkRKYmAhImqB57Tm9qzDwh4WIiUxsBARtaA9K926T2tmDwuRshhYiIha4MtuzQB7WIiUxsBCRNSCOks7dmtm0S1R0DCwEBG1wD2AtLbSrXtg4TosRMpiYCEiagHXYSEKLQwsREQt8FzptpXAwr2EiIKGgYWIqAXt262Z05qJgoWBhYioBY4AIgiAQceF44jUxsBCRNQCRwAx6DQQBKHFY9jDQhQ8DCxERC1wzBJqreAWcIQZx/HsYSFSEgMLEVELHD0mrRXcAoAgCM7hIjN7WIgUxcBCRNQCx5CQtx4W98c5JESkLAYWIqIWOKYpt1Zw6+CY2syiWyJlMbAQETVht4uwWNvbwyJ9jHJpfiJlMbAQETVhtra9aJwDh4SIgoOBhYioCc9l+b1/TBqiXENCoigq2i6iSMbAQkTURF079hFyPu5W42Lm1GYixTCwEBE10Z6ND1t6nMNCRMphYCEiasJ9xk9bQ0Jcnp8oOBhYiIiacJ/xwx4WotDAwEJE1IRPQ0I6t8DCqc1EimFgISJqwiOw6Nq3Dov0PA4JESmFgYWIqAnfalg4JEQUDAwsRERNcJYQUehhYCEiasK9h6W9K902fR4RyYuBhYioCfeeEoMP05rNLLolUgwDCxFREz6tdMshIaKgYGAhImrC7FNg4SwhomBgYCEiaqLebU8g972CWuKxDgt7WIgUw8BCRNSEe/Aw6ds/JFTHwEKkGAYWIqIm6iztHxIycEiIKCgYWIiImvAcEmLRLVEoYGAhImrCc+G49tewcFozkXIYWIiImvCthoVDQkTBwMBCRNSELzUsHBIiCg4GFiKiJhyzfaK0AqK03PyQKBQwsBARNeEILG31rkjHcEiIKBgYWIiImqhvHBJqa+NDoMnCcSy6JVIMAwsRUROOac1tFdwCgEYjQN+4Gi57WIiUw8BCRNREnQ89LIBr+X4za1iIFBMSgWXp0qUYNGgQ4uPjER8fj9zcXHz55ZdqN4uIIpAois4aFkN7A0vjcSy6JVJOSASWzp07Y/HixdixYwe2b9+OX/ziF7j55puxd+9etZtGRBHG7LbKramNReMcHIGFewkRKUendgMAYOrUqR63X3zxRSxduhSbN29G//79VWoVEUUi9zVY2j0kFMUaFiKlhURgcWez2bBq1SrU1NQgNze3xWPMZjPMZrPzdmVlZbCaR0Rhrs6HVW4dnENCVhtEUYQgCIq0jSiShcSQEADs3r0bsbGxMBgMmD17NlavXo1+/fq1eOyiRYuQkJDgvGRnZwe5tUQUruoa2r/KrfO4xqnNoghYbOxlIVJCyASWPn36oLCwEFu2bMGcOXMwc+ZM7Nu3r8VjFyxYgIqKCuelqKgoyK0lonDlz5CQgYvHESkuZIaE9Ho9evbsCQAYNmwYtm3bhtdffx3vvvtus2MNBgMMBkOwm0hEEcBj40MfZwkBjVObTVGyt4so0oVMD0tTdrvdo06FiCgYAqlhAdjDQqSUkOhhWbBgAaZMmYIuXbqgqqoKH3/8MQoKCvDVV1+p3TQiijC+7NTsPE7nNiTE5fmJFBESgaWkpAT33HMPzp07h4SEBAwaNAhfffUVrr32WrWbRkQRpi7AISEuHkekjIACS0NDA4qLi1FbW4u0tDQkJyf79Tp/+9vfAmkGEZFs6v0aEmLRLZHSfK5hqaqqwtKlSzFu3DjEx8ejW7du6Nu3L9LS0tC1a1c88MAD2LZtmxJtJSJSnD+zhEzsYSFSnE+B5ZVXXkG3bt2Ql5eHiRMnYs2aNSgsLMShQ4ewadMmPPfcc7BarbjuuuswefJkHD58WKl2ExEpos6th6S9NSzuew5xeX4iZfg0JLRt2zZs3Lix1eXyR44ciV//+tdYtmwZ8vLy8N1336FXr16yNJSIKBj8mSUU7Xacew8NEcnHp8CyfPnydh3nWK2WiKij8WcdFvfAUsvAQqSIkF2HhYhIDf4EFpPe9bdfrcUqe5uIKIBZQkuWLEFhYSGKi4thMpnQr18/3HLLLa1uWEhE1BF4FN3q2/c3XXQUh4SIlOZ3D8ubb76J0tJSpKenAwBWrFiBq666CpMnT0ZFRYVsDSQiCiZ/Nj/0GBJi0S2RIvzuYWlpw8HNmzdjzpw5mDt3Lj766KOAGkZEpAb/hoTYw0KkNFlXuh09ejTy8vIwduxYOV+WiCho/JslxBoWIqXJEljy8vIQFxcHo9GINWvWICUlRY6XJSIKOo+9hHScJUQUKmQJLFu2bMGqVatQXl6OG264Af/+97/leFkioqBzLBxn0Gmg0Qjteg6HhIiUJ8u05mXLlqG0tBSff/45jh07hp07d8rxskREQeeoYWnvcBDQZOE4Ft0SKcLvwDJ27Fhs2bLFeVsQBEyZMgUfffQRFixYIEvjiIiCzdFD0t6CW8Bz6IhDQkTK8HtIqH///rjyyisxcuRI3HrrrRg4cCBiY2OxfPly1NXVydlGIqKgcfSQ+BJYNBoBxigN6hvsHBIiUojfgWXp0qV4+OGH8dJLL+GFF15AVVUVAKmn5S9/+YtsDSQiCiZHYGnvGiwO0Xod6hssqG3gLCEiJQRUdNu/f3/k5+fjb3/7G44ePYry8nJ07doVGRkZcrWPiChobHYRFqtUdOtLDQvg6pFhDwuRMnwKLKdOnUKXLl2a3a/VatG7d+9m9585cwaXXXaZ/60jIgoiz1VufSvxcxTesoaFSBk+/USOGDECDz30ELZt29bqMRUVFXj//fcxYMAA/Otf/wq4gUREwVJrdg3nxOh964B2BJa6BhtEUZS1XUTkYw/Lvn378OKLL+Laa6+F0WjEsGHD0KlTJxiNRpSVlWHfvn3Yu3cvhg4diiVLluD6669Xqt1ERLJz7x2JMfgWWBxDSKII1DfYfR5SIiLvfOphSUlJwSuvvIJz587hrbfeQq9evVBaWorDhw8DAGbMmIEdO3Zg06ZNDCtE1OHUuC2rH+1j4ODy/ETK8qvo1mQy4bbbbsNtt90md3uIiFTj3sPia2AxNVmenxuUEMlLlpVuiYjCQY3ZvYfFxxqWKK52S6SkgKY1r1+/HuvXr0dJSQnsdrvHYx9++GFADSMiCjbPGhZfh4S4nxCRkvwOLAsXLsQLL7yA4cOHIysrC4LQvk3CiIhCleeQkK9Ft+41LAwsRHLzO7AsW7YM+fn5uPvuu+VsDxGRatyLZQPqYeFqt0Sy87uGxWKxYMyYMXK2hYhIVTVmV8+IKcq/dVgA9rAQKcHvwHL//ffj448/lrMtRESqCqSHpeksISKSl09/QsyfP9953W6347333sPXX3+NQYMGISoqyuPYV155RZ4WEhEFiXsPi881LFEsuiVSkk8/kbt27fK4PWTIEADAnj17PO5nAS4RdURy1bCwh4VIfj4Flm+//dZ5/dSpU+jcuTM0Gs9RJVEUUVRUJE/riIiCyGNacwCzhOq40i2R7PyuYcnJyUFpaWmz+y9duoScnJyAGkVEpIbagJbmZw8LkZL8Diyt7UZaXV0No9Hod4OIiNQiVw1LLVe6JZKdz+uwOApvBUHAs88+i+joaOdjNpsNW7Zscda2EBF1JI4eFkEAjFG+/T3HlW6JlOVzYHEU3oqiiN27d0Ov1zsf0+v1GDx4MB577DH5WkhEFCQ1jUEjRq/zefJArMH1ceq+JxERycPnwOIovL333nvx+uuvIz4+XvZGERGpobYxaPhavwIAMe6BhUW3RLLze2n+vLw8OdtBRKQ6R+2Je/hor2i9FoIAiCJQXc/AQiS3gHZrBoB9+/bh1KlTsFgsHvffdNNNgb40EVFQ1TYW3boX0LaXIAiI0etQbbaimkNCRLLzO7AcO3YM06dPx+7duyEIgnPWkGPc12Zj0RkRdRwWqx0Wmx2A74vGOcQYtKg2Wz1mGxGRPPye1vzoo48iJycHJSUliI6Oxt69e7Fx40YMHz4cBQUFMjaRiEh57jN7fJ3S7OAovGXRLZH8/O5h2bRpE7755hukpqZCo9FAo9HgqquuwqJFi/Db3/622TL+REShrCaAZfkdHIGl2mKFKIrcpoRIRn73sNhsNsTFxQEAUlNTcfbsWQBA165dcfDgQXlaR0QUJJ6r3Pr3t5yjWFcUudotkdz87mEZMGAAfvrpJ+Tk5GDUqFFYsmQJ9Ho93nvvPXTv3l3ONhIRKa7WY0jI3xoWz7VY/JltREQt8/un6Y9//CNqamoAAC+88AJuvPFGXH311UhJScHKlStlayARUTAEsiy/g/vicdVmK9IDbhUROfgdWCZNmuS83rNnTxw4cACXLl1CUlISx22JqMNxHxKK8bOHxXO1Ww4JEcnJ78By8eJFpKSkAACKiorw/vvvo76+HlOnTsXVV18tWwOJiIKhxn1IyM+hHPchoCpzQ8BtIiIXn4tud+/ejW7duiE9PR2XX345CgsLMWLECLz66qt49913MWHCBKxZs0aBphIRKafW7F50628Pi+t57GEhkpfPgeWJJ57AwIEDsXHjRowfPx433ngjbrjhBlRUVKCsrAwPPfQQFi9erERbiYgUU+W2nH6cMfAeFq7FQiQvn38qt23bhm+++QaDBg3C4MGD8d577+E3v/kNNBop+zzyyCMYPXq07A0lIlJSldk9sET59RpNi26JSD4+97BcunQJmZmZAIDY2FjExMQgKSnJ+XhSUhKqqqrkayERURC4b1gY62cNSyx7WIgU49fCcU1nAXFWEBF1dFX1riJZOYaE2MNCJC+/fipnzZoFg8EAAKivr8fs2bMRExMDADCbzfK1jogoSKrN8tawMLAQycvnn8qZM2d63P5//+//NTvmnnvu8b9FREQqqOKQEFFI8/mnMi8vT4l2EBGpylF0KwhAjL8r3Rq5cByRUvze/JCIKJxUN9awxOp10Gj8q8uL1bsvHMceFiI5MbAQEcE1JORv/QoAxHgsHMfAQiQnBhYiIriKZGMDCCw6rQYGnfSxysBCJK+QCCyLFi3CiBEjEBcXh/T0dEybNg0HDx5Uu1lEFCGsNjtqG/cS8rfg1sHxfM4SIpJXSASWDRs2YO7cudi8eTPWrVuHhoYGXHfddaipqVG7aUQUAdwLZP1d5dbB0UPDHhYieQX2p4RM1q5d63E7Pz8f6enp2LFjB8aOHdvseLPZ7LHeS2VlpeJtJKLw5b6zciBDQoBrhhF7WIjkFRI9LE1VVFQAAJKTk1t8fNGiRUhISHBesrOzg9k8Igoz7muwxAcYWByBp8Emor6BU5uJ5BJygcVut2PevHm48sorMWDAgBaPWbBgASoqKpyXoqKiILeSiMKJe29IoDUsCSbXkFKl23L/RBSYkBgScjd37lzs2bMH33//favHGAwG59YARESB8txHKLAalni351fWNSA9zhjQ6xGRJKQCy8MPP4zPP/8cGzduROfOndVuDhFFCDmW5XeIN7meX1HHOhYiuYREYBFFEY888ghWr16NgoIC5OTkqN0kIoogHoElwBoWjx4WDgkRySYkAsvcuXPx8ccf49NPP0VcXByKi4sBAAkJCTCZTCq3jojCnXsNS6BFtx41LHUMLERyCYmi26VLl6KiogLjx49HVlaW87Jy5Uq1m0ZEEaDaY0gowBoWBhYiRYRED4soimo3gYgimGfRbaBDQq7nV9azhoVILiHRw0JEpCb3nZUDrmFhDwuRIhhYiCjiuRfdBtrDwnVYiJTBwEJEEc9jSEjGGpYK9rAQyYaBhYginmO9FL1OA2NUYB+LHjUsXIeFSDYMLEQU8SpqLQCARFMUBEEI6LViDTpoGl+CQ0JE8mFgIaKIV944dJMYHdhwEAAIguAcFmLRLZF8GFiIKKKZrTbUWqRdld0LZgPhWO2WNSxE8mFgIaKI5h4qEkx6WV7TsZ9QZb2V60wRyYSBhYgiWkWtK7DIMSQEuHpqbHbR2XtDRIFhYCGiiFbu1sOSKPOQEMDCWyK5MLAQUURToofFPbCwjoVIHgwsRBTR3HtYEqLlrWEBuBYLkVwYWIgoopU3rsECyDdLKIH7CRHJjoGFiCJahRI1LG6vU87AQiQLBhYiimjlCtSwJLkNLbn34BCR/xhYiCiiec4SkqeGJTnG9TqXahhYiOTAwEJEEc2jhkWBHhYGFiJ5MLAQUURz1LBoBCDOoGvj6PZJiWVgIZIbAwsRRTRHYEkwRUGjCWynZgf3Wpgy1rAQyYKBhYgimqPoVq4pzQBg0GkR29hbwx4WInkwsBBRxLLZRefS+XItGueQFCMFoLJaTmsmkgMDCxFFrKr6Bjg2U5azhwUAkhsDUHmtBTY7d2wmChQDCxFFrItuwzUpMXL3sEivZxe52i2RHBhYiChiXaxWLrAkuw0xXWQdC1HAGFiIKGJdrDY7r6fEGmR9bffF4zhTiChwDCxEFLFK3QJLaqwyQ0IAZwoRyYGBhYgiVqnbkFCqkj0sDCxEAWNgIaKIdbHGfUhI5h4W9+X5OSREFDAGFiKKWB5Ft+xhIQppDCxEFLEUnSUU41rX5VINpzUTBYqBhYgiVmnjkFCsQQdjlFbW107ymNZs9nIkEbUHAwsRRSxHD4vc9SuAFFh0jZspXqhiYCEKFAMLEUUki9Xu3KlZ7uEgANBoBOfMoxIGFqKAMbAQUURyX8xN7inNDunx0uterDZzPyGiADGwEFFEch+mkXuGkEN6nPS6dtFzVV0i8h0DCxFFJPf9feRe5dYhLc7ovM5hIaLAMLAQUUTy2EdIgRoWwNXDAgAlVfWKvAdRpGBgIaKIVKrgxocOjhoWACipZA8LUSAYWIgoIhVXuAJERrzRy5H+S4t172FhYCEKBAMLEUWk85WuIZqsBGUCS3q8ew0Lh4SIAsHAQkQR6VxFnfO6+9CNnDxqWDgkRBQQBhYiikjnGwNEcoweBp28y/I7pHJIiEg2DCxEFHHsdtE5JJSpUP0KAOh1GueuzVyenygwDCxEFHFKa8ywNq48m6lQ/YqDY1joQpUZosjVbon8xcBCRBHnfBBmCDk4Cm8tNjvKahsUfS+icMbAQkQRpzgIM4QcOrm9/tnyOi9HEpE3DCxEFHGK3WYIKVnDAgCXJZqc10+XMbAQ+YuBhYgijnsPS4bCPSyXJbkCyxn2sBD5jYGFiCKO+yq3ig8JufWwnGEPC5HfGFiIKOIUV7qCg9JFt+5DQqxhIfIfAwsRRZyz5dKQULRei3ijTtH3ykwwQiNI1zkkROQ/BhYiiig2u+gcmumSHA1BEBR9vyitxlnYy8BC5D8GFiKKKOcr62Gx2QEA2cnRQXlPR+HtpRoLai3WoLwnUbhhYCGiiHLqUq3zenZScAJLJ486Fu7aTOQPBhYiiijugaVLssnLkfJxL7zlsBCRf0IisGzcuBFTp05Fp06dIAgC1qxZo3aTiChMnXYPLCnBHRICgNNltV6OJKLWhERgqampweDBg/H222+r3RQiCnNqDAl1TY5xXj95kYGFyB/KzudrpylTpmDKlClqN4OIIoB7YOkcpMDSLdX1Pscu1ATlPYnCTUgEFl+ZzWaYza6VKisrK1VsDRF1JEWNU5rT4www6bVBec9OCSbodRpYrHacuMjAQuSPkBgS8tWiRYuQkJDgvGRnZ6vdJCLqAOosNlyokv7YCdaUZgDQaATkpEjDQqcu1sJmF4P23kThokMGlgULFqCiosJ5KSoqUrtJRNQBnLzk6t3oEsTAAriGhSw2O5foJ/JDhxwSMhgMMBgMajeDiDqYIyXVzuvdU2O8HCm/nNRYAOcBAMdKa4Law0MUDjpkDwsRkT/cA0vP9NigvneOW+Ht8QvVXo4kopaERA9LdXU1jhw54rx9/PhxFBYWIjk5GV26dFGxZUQUTtQNLK73O8GpzUQ+C4nAsn37dkyYMMF5e/78+QCAmTNnIj8/X6VWEVG4cQQWrUZA15RgDwm53u8oe1iIfBYSgWX8+PEQRVbNE5FybHYRx0qlotuuKdHQ64I7Ip4aq0e8UYfKeisOn2dgIfIVa1iIKCKcLquFxSrt0twzLbjDQQAgCAIuz4oHABRX1qO81hL0NhB1ZAwsRBQR1Kxfcbg8M855/UBxlSptIOqoGFiIKCKERmCJd14/cI4rdBP5goGFiCLCPreA0DsjzsuRyrk8y/W+B8+zh4XIFwwsRBQR9pypAADotRrVAksft/fdfy5CAkvxbmDZVcAXj6ndEurgGFiIKOzVWqzOGUJ9MuOCPkPIIcagc24JcOh8FeyRsKdQ/g1SaNn2PlC8R+3WUAfGwEJEYW//uUo4Vk7o3yne+8EKcxTe1lpskbFzc31Fy9eJfMTAQkRhb88ZV/1K/8sSVGwJMKiz6/1/Ol2uXkPUYFT33546NgYWIgp7jvoVABigcg/LkOwk5/Vdp8rVawhRB8PAQkRhb89ZqYdFqxHQN0vdwDIoOwGCIF0vLCpXtS1BJ9rVbgF1YAwsRBTWqs1WHCyWAkuv9FgYo7SqtifeGIUejSvt7j9XifoGm6rtUVRDnedtMYzPlRTHwEJEYW3XqTI4JuOM6JasbmMaDclOBAA02ETsPRvGC8id+8nzNntYKAAMLEQU1radKHNeH94tycuRweMILIAUqMLWka89b3OTWwoAAwsRhbXtJy45rw8PkR4W9+C0+dglL0d2YLWXgO15nvexh4UCwMBCRGGrwWZ3FrZ2SjDiskSTug1q1Ds9DskxegDAlmMXYbWF2S/yunJgxQygttTzfgYWCgADC4W3/Z8D744DCper3RJSwd6zlai1SIWew0KkdwUANBoBud1TAABVZmv41LE01AO7/g4svRI49WPzxxlYKAA6tRtApKiVM6Sva2YDg+4ENMzokWTjoQvO646AECpye6Tgi93nAACbjl3EYLe6lg5DFIGqc8CJH4DjBcD+zzxXszUmAlmDgeMbpNt2zhIi/zGwUOS4dBRI7aV2KyiI3APL2N6pKrakuTE9XAHqhyOlmD2uh4qt8cJuB2ouABWngYoi6Wv5KaBkn3Spvdjy83pOBG58VapjcQQW9rBQABhYKHL8tAK45hm1W0FBUlHXgF2N9Svd02LQOSla3QY1kZMag6wEI85V1GPL8UuoMVsRY5DhI1kUAasZaKhtvNS5vlpqGm/XuT3e+Ji5Gqi7BNSVSQWzdWWNt8sBtHN2T1QM0HcqMGwW0DVXuk9w69VkYKEAMLBQ5PjuZaDsBDBsJtAlF9BGqd0iUtCPR0pha1yAZVzvNJVb05wgCLimbzo+2nwKFqsd3x0uxeR+adIQS3mRVLBaV+Z5cQaOWqlexBlI6jzDSXsDRqBi0oGMfsBlw4BuVwPZowB9k2CocVuoj4GFAsDAQuEtNhOoLnbd3vNP6aIzAZ2GABkDgOQcICkHSMyWPoCjUwAtfzQ6um8OlDivjw3BwIL6StwZvwdpuv9goHAMQz4tBj4pBexWtVsmMSYApmTAlATEpAEJnT0vqb2BmHYMs3n0sHAdFvIfP5UpvLkvBW5Klrq4AcBaB5zaJF2aEYDoZOlD2pQMGOMBQxxgcHyNkz7MDXFAlAmIigZ0RulrlLHJdROgM8C5eQwFRYPNjv/sOw8AiNFrQ6fgtqEe2PMvYPcq4MT3GGhvwEDHp3CDH68naBv/r5maXGJc1/Uxrv+nzmOjmzxmAvSxUjgxJUv/v+UK7RwSIpkwsFB4c3xAJnUD5vwIHPxSupzeBpSfbO1JUiFha8WEPhOkXwg6o/RVq5dCjFbveV1nkIaptAbv92n1gE7fzvscr2OUruuM0uuFeYDadPQiKuqkBPCLvhmq7x8EqwXY+h7ww2tSAWsLKkUTNMk5iE1v7O2Ly5Rm2ZiSGi+JjSHZLXR0hGFN9/9r3EuIAsDAQuHNMY1S0Ep/TQ68TboAQE0pcPEIcOk4UHYcqDwr/TKpuQBUXwBqSgBrvQyNEF3FjXVtH604QeMWYEyuIOPoHWrP/foY6S9yQ2zj17jmt1X8ZfrlnnPO69cPyFStHQCAkgPAqlnAhf2e9ydkA32mYDv64nffAUViOu64LBtLbhusSjMVwx4WkgkDC4U3xwekpoW/sGNSpUuX0a0/v6EeMFcB5srGSxVQ3/jVXOUqdLTWuYogrfWuQkiP643H2CzSxWoG7P6MAwRItLsCFBTcx0ZrcAUYU5I0zGZKlmqEohu/mpKkr7EZQMJl0rBbgL0/ZqsNa/dIdUumKC3G90mX42z8c+g/UlhpqGm8QwD6TwNG/wboPAIQBPS32FC25WvAbMWXu4vxws0D1O8RkhMDC8mEgYXCm+MDUvDzF0BUYw9DrEJFm3a7FFqsZleIsZkBW3vus3g+brU0v8/xHKtZCk/Or/Wu2w11jffXyfsLxWYGas3S0Fqrw29N6GOB+MuA+E7S18QuQGpPILUPkNJDGgppw9f7SlBWKwXBa/tlwKRX6Zf/4a+lhQttFul2xgDg5reATld4HGbSazF5QCb+ueM0qsxWrN9fghsGZanQYIUInCVE8mBgofDmHBIK0RVuNRpA01h3EgpsDS0EmXrPi6MnyVwFWKql9Tss1S3crgYsjT1RdeXtq1+wVAOlB6VLM4IUYNL7Ap2GSlNpLxsq9da4+cf2Iuf1O0dkB/bv4a/Sw8Cqma6w0u9mYNqy5lN+G02/4jL8c8dpAMDyrafCLLCwh4XkwcBC4c3xS5JL8rePNkq6GOLkfV27XRpSq73YuDDZRWlxMkdxc1UxUHlaqiOqOCP19jQjSj015SeBQ2tdd6f1BXpeA/T4Bc4kDsXGw1JRa3aySZ3ZQQ310jCQpVq63XcqcOuHXmfd5HZPQdeUaJy8WIvvj5Ti6IVq9EiLDU57lcbAQjJhYKHw5l50S+rRaKRZLqbEto8VRSnUVJ6RFvorPST1WDi+mptsFHhhv3TZ9BZSNdFYoh2O1farkDv0Zmg0KsyG2vQmcH6PdD21DzD93TanCGs0Au4e3RV//kIqzP3fTSfx/E39lW5pcLgHFjsDC/mPgYXCm7OGhT0sHYbQuA5OdDKQOdDzMVGUZnSd2Qmc3g4UbQHO7oJjZVeDvRa36zbidmyEdc9yIOFhYPCvWh2KkV3lOeC7VxvPQwvc9qE0o6odbh+WjZf/cxD1DXas2l6ER6/phaQYvYKNDRL2sJBM+ClO4UsU4VyivKVZQtTxCAKQ3F2amj5lMfDgt8ATx4Db8nAoayoqRVdRrq78OPDF74HXBwM7/zc4f91vXOKaETT810DmgHY/NSE6CrcPk2puaiw25P14QoEGqsBjHRYGFvIfAwuFL/et7DkkFL6ik1Hb+yb86sJMjDAvxW8sv0XtZVe6Hq8pAf79MPD+BOD8PuXaUXsJKPxYuq6PA8Yv8PklHhrXHbrGYay8H447F7/r0NjDQjJhYKHw5T4rhUNCYS3vhxMorbbADD2EAdMR/cD/AQ9tBC6/0XXQuULgvfHA1veV2dNm+4euhQaH3g3E+F7w2zkpGrcMvQwAUFVvxZvrD8vZQnVw80OSCT/FKXy5fzhySChslVabsWzDUQCARgB+N7G39EDWYOCXfwdmfibNJAKktWH+7zHgyyc8e+ACZbMC2z5ovCEAIx/0+6V+e00vGHTSR3P+jydw7EK1DA1UEXtYSCYMLBS+7OxhiQSLvzyAqnpph+PbhnVGz/Qm04FzxgIPFgCjZrvu2/oe8M97paAhh5PfA1WN2wH0mSLtAO6nzknReHBsdwCA1S7iz1/sh9iRdzn2CCzcS4j8x09xCl/uH47sYQlLm49ddC64FmfU4YnJl7d8YJQRmPJfwLSlgKZxcuS+T6XaFjmKcff8y3V90B0Bv9zscT2QES8tJvjNgRJ8Wng24NdUDXtYSCYMLBS+3D8c2cMSdirrG/D7f/zkvP37a3sjNbaNFYOH/Aq4a6W0gzUA/LQc2PhSYA2xWoD9n0nXo2KAXpMCez0AMQYdnpvqWoflmU/34FxFKOyc6QePwNKBe4pIdfwUp/Dl/pczZwmFFVEU8eyaPThTLv0SH5WTjLtzu7Xvyb0mSuujOH6RFiwCDq/zvzHHN0gL3QHScJBMa75cPzALNw/pBEAqwP3dykI02DpgDwV7WEgmDCwUvjgkFLb++8cTWNM4TBJn0OGvdwyG1pdVbftOBX7xx8YbIrDmN9K0ZH8cWe+63u9m/16jFS/cNACZ8UYAwOZjl/DnzxWclq0UBhaSCQMLhS8W3YaljYcu4AW3X9wv3jIQnZP86NW48ndAr+uk6zUlwFrf100BABwrkL4KGqnAV0YJ0VF4e8YV0Gul/7//vekk/mfTCVnfQ3EMLCQTfopT+GINS9jZcfISZn+0A/bGUog543vgpsGd/HsxjQaY+gZgTJBu/7wCOPGDb69RdV7axwgAOl3Rvr2SfDSsazL+PM21Yu6zn+51Fhp3CB57CXGWEPmPn+IUvjgkFFZ2nCzDzA+3odYifV+v65eBx6/rE9iLxmcB177guv2fP/g2a+j4Btf17uMDa4sXd4zIxm/G93DefuKfP2H51lOKvZ+s2MNCMmFgofDFpfnDxn/2FmPGB5tRbZbWTbm6VyreuOsKeXZjvuJuIKOxB+PsLmDvJ+1/rmM4CFA0sADA45P6YNaYbgAAuwgs+GQ3XvrqQOiv0cLAQjJhYKHwxSGhDs9mF/Hm+sN46KMdqG+Qvp9X9kzBe3cPhzFKphCq0QLX/cl1e+PL7etlEUXgWGMPi84IdB4pT3taIQgCnr2xH+6/yrUo3dvfHsWD/7sDZTUWRd87IAwsJBN+ilP44tL8HVpJZT3u+XAL/rrukHP5jmlDOuHDWSNg0sv8/ew+AcgeJV2/sB849GXbz7l4FKhsrCXpkistTqcwjUbAH2/sh+em9nNugrxu33lMef07/HikVPH39wvXYSGZMLBQ+OKQUIdkt4v4380ncc1fN+CHIxcBSHsEzb+2N169cwgMOgW+l4IAXP171+3vX237Oce+dV3vPk7+Nnlx75U5+HDmCCRFRwEAiivr8asPtmD+ykKUVpuD2pY2cfNDkgkDC4Uvj92aZah1IEWJooiCgyW46e3v8cyaPahqrFdJjzPg7/ePxm+v6QVBye9jr+uA9MbVZU9vk+pZvAlSwW1rJlyeji8fHYvR3ZOd932y6wzGv1SAV9YdQkVdQ9Db1CL37xn3EqIAMLBQ+OKQUIdgt4v49kAJ7nx3M2blbcOeM5XOx24f1hlr541Fbo8U5RsiCMDIB1y3nbsvt8BuA45vlK6bkoDMQcq2rRWZCUb8/f7ReHH6AMQbpT2Sqs1WvLH+MK7+r2/w1/8cRHFFvSptc2INC8lEp3YDiBTDIaGQVl5rwb92nsH/bjqBExdrPR7rlxWPZ6f2w+juQQgq7gbdAax7FjBXArv/CVz7JyA6uflx5wqB+grpererVQ3EWo2AGaO6YlL/TLyy7hD+sa0IVruIynor3vzmCJYWHMWk/pm4bVhnXNUrFVHaIP+dysBCMmFgofDFdVhCTlV9A9bvL8FnP53FxsMX0GDzLMLskRaD+df2wZQBmfJMWfaVPkbaIHHLMsBaDxT+HRjzSPPjjqk7HNSS1FgD/jJ9IOaM64E31h/GJ7vOwGYXYbWL+GL3OXyx+xySoqMwZWAWruuXgdHdU+SbaeUNAwvJhIGFwped05rVZreL2HeuEhsOXcCGQxew82QZrPbmM0Wu7JmCmbndcE3fDN/2BFLCiPulwAIA2/OA0XOlVXHdBXH9FV9lJ0fjpdsH4/fX9cHHW07i462nUFotTXsuq23Ax1tO4eMtp2CM0mB09xSM7ZWG4d2S0DcrXpneFwYWkgkDC4Uvkbs1B1t5rQWFReXYdaocu4rKUXiqDJX11haPzYw34sZBWbhzRDZ6ZcQFuaVepPaS9gQ6vhG4dBQ4sdEzlFhqgVObpesJ2UByd1Wa2ZbMBCPmX9cHD/+iFzYcuoB//3QW6/YVO9ezqW+wo+DgBRQcvAAAMEVpMTg7AVd0kcLL5ZlxyEmNCTzEMLCQTBhYKHx5DAmxh0VOFbUNOH6xBofOV+FQcRUOlVTjUHEViiu9F3h2S4nGuN5puH5gFkZ0S1Zn2Kc9hv/aVVS7/UPPwHLie8DWOHW4x4SQn4Gm12lwbb8MXNsvAzVmKzYekkJKwaESnK90TYGua7Bh87FL2HzMtWu1XqtBz/RY9MqIRdfkaHRJiUGX5Gh0TYlGWqyhfd8/9z8WfNn2gKgJBhYKX9yt2S8NNjtKq824UGVGSaUZZyvqUHSpFkWX6lBUVotTl2pR1UqvSVOpsXoM7ZKEq3ulYmzvNHRNiVG49TLpcwMQky7t4nzgC6CqGIjLlB47/B/Xcb0mqdM+P8UYdJgyMAtTBmZBFEUcKK7C1uOXsP1kGXaeLMOZ8jqP4y02O/adq8S+c5XNXsug0yA93oD0OCPS4wxIizMgPc6AxGg9YgxaROt1MEZp0XCiBBMdT2IPCwWAgYXCl8hZQg02OyrrGlBR14Dyxq8VtY1f6xpQXtuA8loLSqqkgHKh2oxLfi7znmCKQu+MWAy4TBpWuCI7EZ2TTMqunaIUnR4Yejfw3V8BuxXY+b/AuMelHoJDa6VjNFFBXzBOToIgoG9WPPpmxWNm4x5F5yrqsOdMJQ4WV2J/cRUOFlfh2IVqtFB2BLPVLoXYS3XNH3QzWDiGiQbpelW9BSE0+EcdTEgFlrfffhsvvfQSiouLMXjwYLz55psYOVLZ/TkojIXwOiyiKKLBJsJis8PcYGv8anf7aoO5wQ6z2/11FitqzDbUWqyosdhQZ7GhxmxFrcWGGosVtWbpa13j7ep66Tg5aTUCshKMyE6KRpfkaPTKiEWfzDj0zohDepyhY4aT1gybBXz3CgAR2P43abZQ0Ragokh6vPt4wBBev36zEkzISjDh2n4ZzvvqG2woulSLkxel3jXHpehSLUqqzG0uUGd3W+6ruo6BhfwXMoFl5cqVmD9/PpYtW4ZRo0bhtddew6RJk3Dw4EGkp6er3TzqiNzGy3edrsSeTSdgF6WwYBcBuyhCbPzquG23i2iwi7DZ7bDaRVhtImx2EQ02u3OKqNXmesza5Fhr43XpOY2P2USYrXbPcGK1h9y2KnqdBmmxBqTHG9y+GpGZYEB2UjSyk6ORlWCELtjreKglsQtw+Q3Agc+BqnPAtveBs4Wux4f8SrWmBZMxSoteGXGtFkabrTaUVltQUlmPkiozquqtqDFbUWOxot5iw86tZ4DGEcQ6Swhv0kghTxBDZG/yUaNGYcSIEXjrrbcAAHa7HdnZ2XjkkUfw1FNPeX1uZWUlEhISUFFRgfj4eNnatHNtPswlR2V7PQquxNrj6Fv8GQDglYbb8IbtFpVbpDydRkC0XosYgw7Rei0STFFIjNYjwRTlcUmM9ryeFmdEvFEXXj0kcijeDSy7qvn9piRg/oGgbHjY0X333Te4ev10AMAx/eU43/k6lVtEgci9509tH+QDX35/h0QPi8ViwY4dO7BgwQLnfRqNBhMnTsSmTZuaHW82m2E2u6rbKyubF4TJQfh5JXJrf1TktSm4bEHehUKrEaBrvGg1AgxRWui1GhiiNI1ftTB43G78qtM2uc91O1qvRbRBh+goLaINWsTodYgxaGHS6xCjl4oc9boI6f0IlsyBwPD7pCEhd1fNZ1hpp5RYg/N6d8sBdD92QMXWUODkDSy+CInAUlpaCpvNhoyMDI/7MzIycOBA8//cixYtwsKFC4PVPAoD2u5X4ZUrBkMjCBAEqeBQIwCaxq+CIEAAoNMK0Go0iGoMGjqtAJ1GA61GQJTW8bXxMY2m8XEBOq3GI6CwpyKMTF4MlJ0Ajq6XbvebBuTOVbNFHUpOnytQikSkolztplAHFxKBxVcLFizA/PnznbcrKyuRnZ0t+/uYfvEYdl06J/vrUnDFdR6A+f2GqN0M6qh0euD//Qs4uxPQ6KSNDhlI280UHQ3Lb7ejcMc6iJzW3OFdoeJ7h0RgSU1NhVarxfnz5z3uP3/+PDIzM5sdbzAYYDAYmt0vt8uHX6P4exBRByAIwGXD1G5Fh5WQnIYh10ZGkTIpJyQGvPV6PYYNG4b169c777Pb7Vi/fj1yc3NVbBkRERGFgpDoYQGA+fPnY+bMmRg+fDhGjhyJ1157DTU1Nbj33nvVbhoRERGpLGQCy5133okLFy7g2WefRXFxMYYMGYK1a9c2K8QlIiKiyBMy67AEQql1WIiIiEg5vvz+DokaFiIiIiJvGFiIiIgo5DGwEBERUchjYCEiIqKQx8BCREREIY+BhYiIiEIeAwsRERGFPAYWIiIiCnkMLERERBTyQmZp/kA4FuutrKxUuSVERETUXo7f2+1ZdD8sAktVVRUAIDs7W+WWEBERka+qqqqQkJDg9Ziw2EvIbrfj7NmziIuLgyAIsr52ZWUlsrOzUVRUFJb7FPH8Or5wP8dwPz8g/M+R59fxKXWOoiiiqqoKnTp1gkbjvUolLHpYNBoNOnfurOh7xMfHh+1/RIDnFw7C/RzD/fyA8D9Hnl/Hp8Q5ttWz4sCiWyIiIgp5DCxEREQU8hhY2mAwGPDcc8/BYDCo3RRF8Pw6vnA/x3A/PyD8z5Hn1/GFwjmGRdEtERERhTf2sBAREVHIY2AhIiKikMfAQkRERCGPgYWIiIhCHgOLmxMnTuC+++5DTk4OTCYTevTogeeeew4Wi8Xr8+rr6zF37lykpKQgNjYWt956K86fPx+kVvvuxRdfxJgxYxAdHY3ExMR2PWfWrFkQBMHjMnnyZGUb6id/zk8URTz77LPIysqCyWTCxIkTcfjwYWUbGoBLly5hxowZiI+PR2JiIu677z5UV1d7fc748eObfQ9nz54dpBZ79/bbb6Nbt24wGo0YNWoUtm7d6vX4VatW4fLLL4fRaMTAgQPxf//3f0FqqX98Ob/8/Pxm3yej0RjE1vpm48aNmDp1Kjp16gRBELBmzZo2n1NQUIChQ4fCYDCgZ8+eyM/PV7ydgfD1HAsKCpp9DwVBQHFxcXAa7KNFixZhxIgRiIuLQ3p6OqZNm4aDBw+2+bxg/xwysLg5cOAA7HY73n33Xezduxevvvoqli1bhqefftrr8373u9/hs88+w6pVq7BhwwacPXsWt9xyS5Ba7TuLxYLbb78dc+bM8el5kydPxrlz55yX5cuXK9TCwPhzfkuWLMEbb7yBZcuWYcuWLYiJicGkSZNQX1+vYEv9N2PGDOzduxfr1q3D559/jo0bN+LBBx9s83kPPPCAx/dwyZIlQWitdytXrsT8+fPx3HPPYefOnRg8eDAmTZqEkpKSFo//8ccfcdddd+G+++7Drl27MG3aNEybNg179uwJcsvbx9fzA6TVRN2/TydPngxii31TU1ODwYMH4+23327X8cePH8cNN9yACRMmoLCwEPPmzcP999+Pr776SuGW+s/Xc3Q4ePCgx/cxPT1doRYGZsOGDZg7dy42b96MdevWoaGhAddddx1qampafY4qP4ciebVkyRIxJyen1cfLy8vFqKgocdWqVc779u/fLwIQN23aFIwm+i0vL09MSEho17EzZ84Ub775ZkXbI7f2np/dbhczMzPFl156yXlfeXm5aDAYxOXLlyvYQv/s27dPBCBu27bNed+XX34pCoIgnjlzptXnjRs3Tnz00UeD0ELfjBw5Upw7d67zts1mEzt16iQuWrSoxePvuOMO8YYbbvC4b9SoUeJDDz2kaDv95ev5+fJzGWoAiKtXr/Z6zBNPPCH279/f474777xTnDRpkoItk097zvHbb78VAYhlZWVBaZPcSkpKRADihg0bWj1GjZ9D9rC0oaKiAsnJya0+vmPHDjQ0NGDixInO+y6//HJ06dIFmzZtCkYTg6agoADp6eno06cP5syZg4sXL6rdJFkcP34cxcXFHt/DhIQEjBo1KiS/h5s2bUJiYiKGDx/uvG/ixInQaDTYsmWL1+f+/e9/R2pqKgYMGIAFCxagtrZW6eZ6ZbFYsGPHDo9/e41Gg4kTJ7b6b79p0yaP4wFg0qRJIfm98uf8AKC6uhpdu3ZFdnY2br75ZuzduzcYzQ2KjvT9C9SQIUOQlZWFa6+9Fj/88IPazWm3iooKAPD6u0+N72NYbH6olCNHjuDNN9/Eyy+/3OoxxcXF0Ov1zWolMjIyQna80h+TJ0/GLbfcgpycHBw9ehRPP/00pkyZgk2bNkGr1ardvIA4vk8ZGRke94fq97C4uLhZ17JOp0NycrLX9v7qV79C165d0alTJ/z888948skncfDgQXzyySdKN7lVpaWlsNlsLf7bHzhwoMXnFBcXd5jvlT/n16dPH3z44YcYNGgQKioq8PLLL2PMmDHYu3ev4pu8BkNr37/KykrU1dXBZDKp1DL5ZGVlYdmyZRg+fDjMZjM++OADjB8/Hlu2bMHQoUPVbp5Xdrsd8+bNw5VXXokBAwa0epwaP4cR0cPy1FNPtVgA5X5p+uFx5swZTJ48GbfffjseeOABlVrefv6coy9++ctf4qabbsLAgQMxbdo0fP7559i2bRsKCgrkOwkvlD6/UKD0OT744IOYNGkSBg4ciBkzZuB//ud/sHr1ahw9elTGs6BA5ebm4p577sGQIUMwbtw4fPLJJ0hLS8O7776rdtOonfr06YOHHnoIw4YNw5gxY/Dhhx9izJgxePXVV9VuWpvmzp2LPXv2YMWKFWo3pZmI6GH5/e9/j1mzZnk9pnv37s7rZ8+exYQJEzBmzBi89957Xp+XmZkJi8WC8vJyj16W8+fPIzMzM5Bm+8TXcwxU9+7dkZqaiiNHjuCaa66R7XVbo+T5Ob5P58+fR1ZWlvP+8+fPY8iQIX69pj/ae46ZmZnNCjatVisuXbrk0/+5UaNGAZB6Env06OFze+WQmpoKrVbbbFadt5+fzMxMn45Xkz/n11RUVBSuuOIKHDlyRIkmBl1r37/4+Piw6F1pzciRI/H999+r3QyvHn74YWcRf1u9eWr8HEZEYElLS0NaWlq7jj1z5gwmTJiAYcOGIS8vDxqN906oYcOGISoqCuvXr8ett94KQKoMP3XqFHJzcwNue3v5co5yOH36NC5evOjxC15JSp5fTk4OMjMzsX79emdAqaysxJYtW3yeSRWI9p5jbm4uysvLsWPHDgwbNgwA8M0338ButztDSHsUFhYCQNC+hy3R6/UYNmwY1q9fj2nTpgGQuqTXr1+Phx9+uMXn5ObmYv369Zg3b57zvnXr1gX15629/Dm/pmw2G3bv3o3rr79ewZYGT25ubrPpr6H6/ZNTYWGhqj9r3oiiiEceeQSrV69GQUEBcnJy2nyOKj+HipXzdkCnT58We/bsKV5zzTXi6dOnxXPnzjkv7sf06dNH3LJli/O+2bNni126dBG/+eYbcfv27WJubq6Ym5urxim0y8mTJ8Vdu3aJCxcuFGNjY8Vdu3aJu3btEquqqpzH9OnTR/zkk09EURTFqqoq8bHHHhM3bdokHj9+XPz666/FoUOHir169RLr6+vVOo1W+Xp+oiiKixcvFhMTE8VPP/1U/Pnnn8Wbb75ZzMnJEevq6tQ4hTZNnjxZvOKKK8QtW7aI33//vdirVy/xrrvucj7e9P/pkSNHxBdeeEHcvn27ePz4cfHTTz8Vu3fvLo4dO1atU3BasWKFaDAYxPz8fHHfvn3igw8+KCYmJorFxcWiKIri3XffLT711FPO43/44QdRp9OJL7/8srh//37xueeeE6OiosTdu3erdQpe+Xp+CxcuFL/66ivx6NGj4o4dO8Rf/vKXotFoFPfu3avWKXhVVVXl/BkDIL7yyivirl27xJMnT4qiKIpPPfWUePfddzuPP3bsmBgdHS0+/vjj4v79+8W3335b1Gq14tq1a9U6hTb5eo6vvvqquGbNGvHw4cPi7t27xUcffVTUaDTi119/rdYpeDVnzhwxISFBLCgo8Pi9V1tb6zwmFH4OGVjc5OXliQBavDgcP35cBCB+++23zvvq6urE3/zmN2JSUpIYHR0tTp8+3SPkhJqZM2e2eI7u5wRAzMvLE0VRFGtra8XrrrtOTEtLE6OiosSuXbuKDzzwgPMDN9T4en6iKE1tfuaZZ8SMjAzRYDCI11xzjXjw4MHgN76dLl68KN51111ibGysGB8fL957770egazp/9NTp06JY8eOFZOTk0WDwSD27NlTfPzxx8WKigqVzsDTm2++KXbp0kXU6/XiyJEjxc2bNzsfGzdunDhz5kyP4//xj3+IvXv3FvV6vdi/f3/xiy++CHKLfePL+c2bN895bEZGhnj99deLO3fuVKHV7eOYwtv04jinmTNniuPGjWv2nCFDhoh6vV7s3r27x89iKPL1HP/rv/5L7NGjh2g0GsXk5GRx/Pjx4jfffKNO49uhtd977t+XUPg5FBobS0RERBSyImKWEBEREXVsDCxEREQU8hhYiIiIKOQxsBAREVHIY2AhIiKikMfAQkRERCGPgYWIiIhCHgMLERERhTwGFiIiIgp5DCxEREQU8hhYiIiIKOQxsBBRSJozZw6uuuqqFh/r3LkzFi9eHOQWEZGadGo3gIioqb179+K9997Dd9991+Ljffv2RWFhYXAbRUSqYg8LEYWcl156CSNGjMCYMWNafDw5ORnFxcVBbhURqYmBhYhCitVqxSeffIJbb73Ved9DDz2Ev/3tb87bVVVVMJlMajSPiFTCwEJEIeXo0aOoqqrCwIEDAQB2ux2rVq1CXFyc85iff/4Z/fr1U6uJRKQCBhYiCinl5eUAgNjYWADAV199hbKyMhiNRgDA5s2bcebMGUyfPl2tJhKRClh0S0QhpWvXrhAEAcuXL0dMTAwee+wx3HDDDfj000+RnZ2N2bNnY+LEia3OICKi8CSIoiiq3QgiIneLFi3C4sWLYTKZ8Je//AXDhg3DzTffjNLSUkydOhXvvPMOkpKS1G4mEQURAwsRERGFPNawEBERUchjYCEiIqKQx8BCREREIY+BhYiIiEIeAwsRERGFPAYWIiIiCnkMLERERBTyGFiIiIgo5DGwEBERUchjYCEiIqKQx8BCREREIe//Ax9JoZGwnGYxAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters\n", "eps_d, V = 0.3, 0.2\n", "\n", "# Construct and Initialize Gf\n", "w_mesh = MeshReFreq(window=(-2,2), n_w=1000)\n", "G = Gf(mesh=w_mesh, target_shape=[2,2])\n", "G[0,0] << Omega - eps_d\n", "G[0,1] << V\n", "G[1,0] << V\n", "G[1,1] << inverse(Flat(1.0))\n", "G.invert()\n", "\n", "# Plot\n", "oplot(-G[0,0].imag/pi, '-', lw=2, name = \"Impurity\")\n", "oplot(-G[1,1].imag/pi, '-', lw=2, name = \"Bath\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Plot the density $n(\\epsilon)$ as a function of $\\epsilon$ for a Green's function $G = 1/(i\\omega_n - \\epsilon)$. What is the curve that you obtained? How does it change with temperature?" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:03:59.784311Z", "iopub.status.busy": "2023-08-28T15:03:59.784241Z", "iopub.status.idle": "2023-08-28T15:04:00.394631Z", "shell.execute_reply": "2023-08-28T15:04:00.394382Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Consider various temperatures\n", "for beta in [3, 10, 100]:\n", " \n", " # Construct Gf\n", " iw_mesh = MeshImFreq(beta=beta, S='Fermion', n_iw=1000)\n", " G = Gf(mesh=iw_mesh, target_shape=[])\n", " \n", " # Initialize and plot for different epsilon\n", " import numpy\n", " eps_r = numpy.arange(-1,1,0.05)\n", " n_r = []\n", " for eps in eps_r:\n", " G << inverse(iOmega_n - eps)\n", " n_r.append(G.density().real)\n", " plt.plot(eps_r, n_r, lw=2, label=r\"$\\beta = %i$\"%beta)\n", " \n", "plt.xlabel('$\\epsilon$')\n", "plt.ylabel('$n(\\epsilon)$')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Define a block Green's function with an *up* and a *down* block. Each block is just a simple 1x1 imaginary-frequency Green's function. Iterate over the blocks to initialize the two blocks to $1/i \\omega_n$. What happens if you change $\\beta$?" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:04:00.395928Z", "iopub.status.busy": "2023-08-28T15:04:00.395861Z", "iopub.status.idle": "2023-08-28T15:04:00.514514Z", "shell.execute_reply": "2023-08-28T15:04:00.514281Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Im G[$\\\\beta$]')" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Consider various temperatures\n", "for beta in [5, 7, 10]:\n", " iw_mesh = MeshImFreq(beta=beta, S='Fermion', n_iw=1000)\n", " G = BlockGf(mesh=iw_mesh, gf_struct=[('up',1),('down',1)])\n", "\n", " # Loop over the blocks to initialize\n", " for name, g in G:\n", " g << inverse(iOmega_n)\n", " \n", " # Plot one entry\n", " oplot(G[\"up\"][0,0].imag, '-o', name=r\"Im G[$\\beta$={}]\".format(beta))\n", " \n", "plt.xlim(0,5)\n", "plt.ylim(-3.5,0.1)\n", "plt.ylabel(r\"Im G[$\\beta$]\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "Consider a Hubbard atom with $U=2$ at temperature $T = 1/\\beta = 1/10$. The non-interacting and interacting Green's functions for this problem are:\n", "\n", "$$\n", "G_0 = \\frac{1}{i \\omega_n + U/2} \\qquad G = \\frac{1}{2(i\\omega_n + U/2)} + \\frac{1}{2(i\\omega_n - U/2)}\n", "$$\n", "\n", "Using Dyson's equation, verify that the corresponding self-energy is indeed\n", "\n", "$$\n", "\\Sigma = \\frac{U}{2} + \\frac{U^2}{4 i\\omega_n}\n", "$$" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:04:00.515788Z", "iopub.status.busy": "2023-08-28T15:04:00.515719Z", "iopub.status.idle": "2023-08-28T15:04:00.612695Z", "shell.execute_reply": "2023-08-28T15:04:00.612474Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 10.0)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters\n", "U = 2.0\n", "\n", "# Green's function containers\n", "iw_mesh = MeshImFreq(beta=10, S='Fermion', n_iw=1000)\n", "G_0 = Gf(mesh=iw_mesh, target_shape=[])\n", "G = G_0.copy()\n", "Sigma = G_0.copy()\n", "Sigma_check = G_0.copy()\n", "\n", "# Green's functions of the Hubbard atom\n", "G_0 << inverse(iOmega_n + U/2)\n", "G << 0.5*inverse(iOmega_n + U/2) + 0.5*inverse(iOmega_n - U/2)\n", "\n", "# Dyson's equation to find the self-energy\n", "Sigma << inverse(G_0) - inverse(G)\n", "\n", "# Known solution\n", "Sigma_check << U/2 + U*inverse(2*iOmega_n)\n", "\n", "oplot(Sigma_check, '-o', name=r'$\\Sigma$_check')\n", "oplot(Sigma, '-x', name=r'$\\Sigma$')\n", "plt.xlim(0,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 5\n", "\n", "Compute the following second-order self-energy with $U=2$ and $\\beta=50$\n", "\n", "$$ \\Sigma(i\\omega_n) = U^2 \\int_0^\\beta d\\tau e^{i \\omega_n \\tau} G_0(\\tau)^3 $$\n", "\n", "using an non-interacting $G_0$ given by a semi-circular of half-bandwidth 1. Use Dyson's equation to compute $G(i\\omega_n)$.\n", "\n", "Hint: The `SemiCircular` initializer only works for frequency Green's functions.\n", "\n", "Hint: The \"power operator\" is not defined for Green's functions. Use multiplication." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:04:00.613959Z", "iopub.status.busy": "2023-08-28T15:04:00.613893Z", "iopub.status.idle": "2023-08-28T15:04:00.695790Z", "shell.execute_reply": "2023-08-28T15:04:00.695583Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.0, 4.0)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters\n", "U = 2.0\n", "\n", "# Define and initialize G0 in freq\n", "iw_mesh = MeshImFreq(beta=50, S='Fermion', n_iw=1000)\n", "G0_iw = Gf(mesh=iw_mesh, target_shape=[1,1])\n", "G0_iw << SemiCircular(1.0)\n", "\n", "# Compute second-order self-energy\n", "G0_tau = make_gf_from_fourier(G0_iw)\n", "Sigma_tau = U**2 * G0_tau * G0_tau * G0_tau\n", "Sigma_iw = make_gf_from_fourier(Sigma_tau)\n", "\n", "# Dyson's equation\n", "G_iw = G0_iw.copy()\n", "G_iw << inverse(inverse(G0_iw) - Sigma_iw)\n", "\n", "oplot(G_iw, '-o', name='G')\n", "plt.xlim(0,4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6\n", "\n", "Use Pade approximants to obtain a real-frequency version of the Green's function computed in the Exercise 5. What is the effect of interactions at second-order perturbation theory? How is it changing with different values of $U$?" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2023-08-28T15:04:00.697087Z", "iopub.status.busy": "2023-08-28T15:04:00.697010Z", "iopub.status.idle": "2023-08-28T15:04:00.778542Z", "shell.execute_reply": "2023-08-28T15:04:00.778327Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\rho(\\\\omega)$')" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create Green's functions\n", "w_mesh = MeshReFreq(window=(-4,4), n_w=1000)\n", "G_w = Gf(mesh=w_mesh, target_shape=[1,1])\n", "G0_w = G_w.copy()\n", "\n", "# Initialize from Pade\n", "G_w.set_from_pade(G_iw)\n", "oplot(-G_w[0,0].imag/pi, lw=2, name=\"Second-order\")\n", "\n", "# Initialize non-interacting Green's function\n", "G0_w << SemiCircular(1.0)\n", "oplot(-G0_w[0,0].imag/pi, name=\"Non-interacting\")\n", "\n", "plt.ylabel(r\"$\\rho(\\omega)$\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "widgets": { "state": {}, "version": "1.1.1" } }, "nbformat": 4, "nbformat_minor": 4 }