################################################################################
#
# TPRF: Two-Particle Response Function (TPRF) Toolbox for TRIQS
#
# Copyright (C) 2019 by The Simons Foundation
# Author: H. U.R. Strand
#
# TPRF is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# TPRF is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
#
# You should have received a copy of the GNU General Public License along with
# TPRF. If not, see <http://www.gnu.org/licenses/>.
#
################################################################################
import itertools
import numpy as np
# ----------------------------------------------------------------------
import triqs.utility.mpi as mpi
# ----------------------------------------------------------------------
from triqs_tprf.lattice import fourier_wk_to_wr
from triqs_tprf.lattice import fourier_wr_to_wk
from triqs_tprf.lattice import fourier_wr_to_tr
from triqs_tprf.lattice import fourier_tr_to_wr
from triqs_tprf.lattice import chi_wr_from_chi_tr
from triqs_tprf.lattice import chi_tr_from_chi_wr
from triqs_tprf.lattice import chi_wk_from_chi_wr
from triqs_tprf.lattice import chi_wr_from_chi_wk
from triqs_tprf.lattice import chi0_tr_from_grt_PH
from triqs_tprf.lattice import dynamical_screened_interaction_W_wk as cpp_dynamical_screened_interaction_W_wk
from triqs_tprf.lattice import \
dynamical_screened_interaction_W_wk_from_generalized_susceptibility \
as cpp_dynamical_screened_interaction_W_wk_from_generalized_susceptibility
from triqs_tprf.lattice import gw_sigma_wk_serial_fft as cpp_gw_sigma_wk_serial_fft
from triqs_tprf.lattice import gw_sigma_tr as cpp_gw_sigma_tr
# ----------------------------------------------------------------------
[docs]
def bubble_PI_wk(g_wk):
r""" Compute the particle-hole bubble from the single particle lattice Green's function
.. math::
\Pi_{abcd}(i\omega_n, k) = -
\mathcal{F}_{\tau, \mathbf{r} \rightarrow i\omega_n, \mathbf{k}}
\left\{ G_{d\bar{a}}(\tau, \mathbf{r}) G_{b\bar{c}}(-\tau, -\mathbf{r}) \right\}
Parameters
----------
g_wk : TRIQS Green's function (rank 2) on Matsubara and Brillouinzone meshes
Single particle lattice Green's function.
Returns
-------
PI_wk : TRIQS Green's function (rank 4) on Matsubara and Brillouinzone meshes
Particle hole bubble.
"""
nw = len(g_wk.mesh.components[0]) // 2
g_wr = fourier_wk_to_wr(g_wk)
g_tr = fourier_wr_to_tr(g_wr)
del g_wr
PI_tr = chi0_tr_from_grt_PH(g_tr)
del g_tr
PI_wr = chi_wr_from_chi_tr(PI_tr, nw=nw)
del PI_tr
PI_wk = chi_wk_from_chi_wr(PI_wr)
del PI_wr
return PI_wk
# ----------------------------------------------------------------------
def dynamical_screened_interaction_W_wk(PI_wk, V_k):
return cpp_dynamical_screened_interaction_W_wk(PI_wk, V_k)
# ----------------------------------------------------------------------
def dynamical_screened_interaction_W_wk_from_generalized_susceptibility(chi_wk, V_k):
return cpp_dynamical_screened_interaction_W_wk_from_generalized_susceptibility(chi_wk, V_k)
# ----------------------------------------------------------------------
[docs]
def gw_sigma_wk(Wr_wk, g_wk, fft_flag=False):
r""" GW self energy :math:`\Sigma(i\omega_n, \mathbf{k})` calculator
Fourier transforms the screened interaction and the single-particle
Green's function to imagiary time and real space.
.. math::
G_{ab}(\tau, \mathbf{r}) = \mathcal{F}^{-1}
\left\{ G_{ab}(i\omega_n, \mathbf{k}) \right\}
.. math::
W^{(r)}_{abcd}(\tau, \mathbf{r}) = \mathcal{F}^{-1}
\left\{ W^{(r)}_{abcd}(i\omega_n, \mathbf{k}) \right\}
computes the GW self-energy as the product
.. math::
\Sigma_{ab}(\tau, \mathbf{r}) =
\sum_{cd} W^{(r)}_{abcd}(\tau, \mathbf{r}) G_{cd}(\tau, \mathbf{r})
and transforms back to frequency and momentum
.. math::
\Sigma_{ab}(i\omega_n, \mathbf{k}) =
\mathcal{F} \left\{ \Sigma_{ab}(\tau, \mathbf{r}) \right\}
Parameters
----------
V_k : TRIQS Green's function (rank 4) on a Brillouinzone mesh
static bare interaction :math:`V_{abcd}(\mathbf{k})`
Wr_wk : TRIQS Green's function (rank 4) on Matsubara and Brillouinzone meshes
retarded screened interaction :math:`W^{(r)}_{abcd}(i\omega_n, \mathbf{k})`
g_wk : TRIQS Green's function (rank 2) on Matsubara and Brillouinzone meshes
single particle Green's function :math:`G_{ab}(i\omega_n, \mathbf{k})`
Returns
-------
sigma_wk : TRIQS Green's function (rank 2) on Matsubara and Brillouinzone meshes
GW self-energy :math:`\Sigma_{ab}(i\omega_n, \mathbf{k})`
"""
if fft_flag:
nw = len(g_wk.mesh.components[0]) // 2
ntau = nw * 6 + 1
mpi.report('g wk -> wr')
g_wr = fourier_wk_to_wr(g_wk)
mpi.report('g wr -> tr')
g_tr = fourier_wr_to_tr(g_wr, nt=ntau)
del g_wr
mpi.report('W wk -> wr')
Wr_wr = chi_wr_from_chi_wk(Wr_wk)
mpi.report('W wr -> tr')
Wr_tr = chi_tr_from_chi_wr(Wr_wr, ntau=ntau)
del Wr_wr
mpi.report('sigma tr')
sigma_tr = cpp_gw_sigma_tr(Wr_tr, g_tr)
del Wr_tr
del g_tr
mpi.report('sigma tr -> wr')
sigma_wr = fourier_tr_to_wr(sigma_tr, nw=nw)
del sigma_tr
mpi.report('sigma wr -> wk')
sigma_wk = fourier_wr_to_wk(sigma_wr)
del sigma_wr
else:
sigma_wk = cpp_gw_sigma_wk_serial_fft(Wr_wk, g_wk)
return sigma_wk