# Copyright (c) 2013-2015 Commissariat à l'énergie atomique et aux énergies alternatives (CEA)
# Copyright (c) 2013-2015 Centre national de la recherche scientifique (CNRS)
# Copyright (c) 2020-2022 Simons Foundation
#
# This program 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.
#
# This program 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 may obtain a copy of the License at
# https:#www.gnu.org/licenses/gpl-3.0.txt
#
# Authors: Michel Ferrero, Alexander Hampel, Olivier Parcollet, Nils Wentzell
from .sumk_discrete import SumkDiscrete
import numpy as np
from triqs.lattice.tight_binding import TBLattice
[docs]
class SumkDiscreteFromLattice (SumkDiscrete):
r"""
* Computes
.. math::
G \leftarrow \sum_k (\omega + \mu - \epsilon_k - \Sigma(k,\omega))^{-1}
for GF functions with blocks of the size of the matrix eps_k with a discrete sum.
* The object contains the discretized hoppings and points in the arrays
hopping, bz_points,bz_weights,mu_pattern,overlap (IF non orthogonal)
It can also generate a grid (ReComputeGrid) for a regular grid or a Gauss-Legendre sum
for the whole Brillouin Zone or a patch of the BZ.
"""
[docs]
def __init__(self, lattice, patch = None, n_points = 8, method = "Riemann"):
"""
:param lattice: The underlying triqs.lattice or triqs.super_lattice provinding t(k)
:param n_points: Number of points in the BZ in EACH direction
:param method: Riemann (default) or 'Gauss' (not checked)
"""
assert isinstance(lattice,TBLattice), "lattice must be a TBLattice instance"
self.SL = lattice
self.patch,self.method = patch,method
# init the array
SumkDiscrete.__init__ (self, dim = self.SL.ndim, gf_struct = lattice.orbital_names)
self.Recompute_Grid(n_points, method)
#-------------------------------------------------------------
def __reduce__(self):
return self.__class__, (self.SL, self.patch, self.bz_weights.shape[0],self.method)
#-------------------------------------------------------------
[docs]
def Recompute_Grid (self, n_points, method="Riemann", Q=None):
"""(Re)Computes the grid on the patch given at construction:
* n_points: Number of points in the BZ in EACH direction
* method: Riemann (default) or 'Gauss' (not checked)
* Q: anything from which a 1d-array can be computed.
computes t(k+Q) instead of t(k) (useful for bare chi_0)
"""
assert method in ["Riemann","Gauss"], "method %s is not recognized"%method
self.method = method
self.resize_arrays(n_points)
if self.patch:
self.__Compute_Grid_One_patch(self.patch, n_points , method, Q)
else:
self.__Compute_Grid(n_points, method, Q)
#-------------------------------------------------------------
def __Compute_Grid (self, n_bz, method="Riemann", Q=None):
"""
Internal
"""
n_bz_A,n_bz_B, n_bz_C = n_bz, (n_bz if self.dim > 1 else 1), (n_bz if self.dim > 2 else 1)
nk = n_bz_A* n_bz_B* n_bz_C
self.resize_arrays(nk)
# compute the points where to evaluate the function in the BZ and with the weights
def pts1d(N):
for n in range(N):
yield (n - N/2 +1.0) / N
if method=="Riemann":
bz_weights=1.0/nk
k_index =0
for nz in pts1d(n_bz_C):
for ny in pts1d(n_bz_B):
for nx in pts1d(n_bz_A):
self.bz_points[k_index,:] = (nx,ny,nz)[0:self.dim]
k_index +=1
elif method=="Gauss":
assert 0, "Gauss: NR gauleg not checked"
k_index =0
for wa,ptsa in NR.Gauleg(-pi,pi,n_bz_A):
for wb,ptsb in NR.Gauleg(-pi,pi,n_bz_B):
for wc,ptsc in NR.Gauleg(-pi,pi,n_bz_C):
self.bz_points[k_index,:] = (ptsa,ptsb,ptsc)[0:self.dim] /(2*pi)
self.bz_weights[k_index] = wa * wb * wc
k_index +=1
else:
raise IndexError("Summation method unknown")
# A shift
if Q:
try:
Q = np.array(Q)
assert len(Q.shape) ==1
except:
raise RuntimeError("Q is not of correct type")
for k_index in range(self.N_kpts()):
self.bz_points[k_index,:] +=Q
# Compute the discretized hoppings from the Superlattice
self.hopping[:,:,:] = self.SL.fourier(self.bz_points)
if self.orthogonal_basis:
self.mu_pattern[:,:] = np.identity(self.SL.n_orbitals)
else:
assert 0 , "not checked"
self.overlap[:,:,:] = self.SL.Overlap(bz_points.transpose().copy())
mupat = np.identity(self.SL.n_orbitals)
for k_index in range(self.N_kpts()):
self.mu_pattern[:,:,k_index] = np.dot( mupat ,self.Overlap[:,:,k_index])
#-------------------------------------------------------------
def __Compute_Grid_One_patch(self, patch, n_bz, method = "Riemann", Q=None):
"""
Internal
"""
tritemp = np.array(patch._triangles)
ntri = len(tritemp)/3
nk = n_bz*n_bz*ntri
self.resize_arrays(nk)
# Reshape the list to group 3 points together
triangles = tritemp.reshape((ntri,3,2))
total_weight = 0
# Loop over all k-points in the triangles
k_index = 0
for (a,b,c),w in zip(triangles,patch._weights):
g = ((a+b+c)/3.0-a)/n_bz;
for i in range(n_bz):
s = i/float(n_bz)
for j in range(n_bz-i):
t = j/float(n_bz)
for k in range(2):
rv = a+s*(b-a)+t*(c-a)+(k+1)*g
if k == 0 or j < n_bz-i-1:
self.bz_points[k_index] = rv
self.bz_weights[k_index] = w/(n_bz*n_bz)
total_weight += self.bz_weights[k_index]
k_index = k_index+1
# Normalize weights so that they sum up to 1
self.bz_weights /= total_weight
# Compute the discretized hoppings from the Superlattice
self.hopping[:,:,:] = self.SL.fourier(self.bz_points)
if self.orthogonal_basis:
self.mu_pattern[:,:] = self.SL.MuPattern[:,:]
else:
assert 0 , "not checked"