Source code for triqs.sumk.sumk_discrete_from_lattice

# 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 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.
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# You may obtain a copy of the License at
#     https:#www.gnu.org/licenses/gpl-3.0.txt
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# Authors: Michel Ferrero, 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. """ 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"