mirror of
https://github.com/triqs/dft_tools
synced 2024-09-01 16:53:43 +02:00
1157 lines
50 KiB
Python
1157 lines
50 KiB
Python
|
|
################################################################################
|
|
#
|
|
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
#
|
|
# Copyright (C) 2011 by M. Aichhorn, L. Pourovskii, V. Vildosola
|
|
#
|
|
# TRIQS 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.
|
|
#
|
|
# TRIQS 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
|
|
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
|
#
|
|
################################################################################
|
|
|
|
from types import *
|
|
#from pytriqs.applications.dft.symmetry import *
|
|
from symmetry import *
|
|
import numpy
|
|
import pytriqs.utility.dichotomy as dichotomy
|
|
from pytriqs.gf.local import *
|
|
#from pytriqs.applications.impurity_solvers.operators import *
|
|
from pytriqs.operators import *
|
|
from pytriqs.archive import *
|
|
import pytriqs.utility.mpi as mpi
|
|
|
|
from math import cos,sin
|
|
|
|
import string, pickle
|
|
|
|
class SumkLDA:
|
|
"""This class provides a general SumK method for combining ab-initio code and pytriqs."""
|
|
|
|
|
|
def __init__(self, hdf_file, mu = 0.0, h_field = 0.0, use_lda_blocks = False, lda_data = 'SumK_LDA', symm_corr_data = 'SymmCorr',
|
|
par_proj_data = 'SumK_LDA_ParProj', symm_par_data = 'SymmPar', bands_data = 'SumK_LDA_Bands'):
|
|
"""
|
|
Initialises the class from data previously stored into an HDF5
|
|
"""
|
|
|
|
if not (type(hdf_file)==StringType):
|
|
mpi.report("Give a string for the HDF5 filename to read the input!")
|
|
else:
|
|
self.hdf_file = hdf_file
|
|
self.lda_data = lda_data
|
|
self.par_proj_data = par_proj_data
|
|
self.bands_data = bands_data
|
|
self.symm_par_data = symm_par_data
|
|
self.symm_corr_data = symm_corr_data
|
|
self.block_names = [ ['up','down'], ['ud'] ]
|
|
self.n_spin_blocks_gf = [2,1]
|
|
self.Gupf = None
|
|
self.h_field = h_field
|
|
|
|
# read input from HDF:
|
|
things_to_read = ['energy_unit','n_k','k_dep_projection','SP','SO','charge_below','density_required',
|
|
'symm_op','n_shells','shells','n_corr_shells','corr_shells','use_rotations','rot_mat',
|
|
'rot_mat_time_inv','n_reps','dim_reps','T','n_orbitals','proj_mat','bz_weights','hopping']
|
|
optional_things = ['gf_struct_solver','map_inv','map','chemical_potential','dc_imp','dc_energ','deg_shells']
|
|
|
|
#ar=HDFArchive(self.hdf_file,'a')
|
|
#del ar
|
|
|
|
self.retval = self.read_input_from_hdf(subgrp=self.lda_data,things_to_read=things_to_read,optional_things=optional_things)
|
|
|
|
#ar=HDFArchive(self.hdf_file,'a')
|
|
#del ar
|
|
|
|
if (self.SO) and (abs(self.h_field)>0.000001):
|
|
self.h_field=0.0
|
|
mpi.report("For SO, the external magnetic field is not implemented, setting it to 0!!")
|
|
|
|
|
|
self.inequiv_shells(self.corr_shells) # determine the number of inequivalent correlated shells
|
|
|
|
# field to convert block_names to indices
|
|
self.names_to_ind = [{}, {}]
|
|
for ibl in range(2):
|
|
for inm in range(self.n_spin_blocks_gf[ibl]):
|
|
self.names_to_ind[ibl][self.block_names[ibl][inm]] = inm * self.SP #(self.Nspinblocs-1)
|
|
|
|
# GF structure used for the local things in the k sums
|
|
self.gf_struct_corr = [ [ (al, range( self.corr_shells[i][3])) for al in self.block_names[self.corr_shells[i][4]] ]
|
|
for i in xrange(self.n_corr_shells) ]
|
|
|
|
if not (self.retval['gf_struct_solver']):
|
|
# No gf_struct was stored in HDF, so first set a standard one:
|
|
self.gf_struct_solver = [ [ (al, range( self.corr_shells[self.invshellmap[i]][3]) )
|
|
for al in self.block_names[self.corr_shells[self.invshellmap[i]][4]] ]
|
|
for i in xrange(self.n_inequiv_corr_shells) ]
|
|
self.map = [ {} for i in xrange(self.n_inequiv_corr_shells) ]
|
|
self.map_inv = [ {} for i in xrange(self.n_inequiv_corr_shells) ]
|
|
for i in xrange(self.n_inequiv_corr_shells):
|
|
for al in self.block_names[self.corr_shells[self.invshellmap[i]][4]]:
|
|
self.map[i][al] = [al for j in range( self.corr_shells[self.invshellmap[i]][3] ) ]
|
|
self.map_inv[i][al] = al
|
|
|
|
if not (self.retval['dc_imp']):
|
|
# init the double counting:
|
|
self.__init_dc()
|
|
|
|
if not (self.retval['chemical_potential']):
|
|
self.chemical_potential = mu
|
|
|
|
if not (self.retval['deg_shells']):
|
|
self.deg_shells = [ [] for i in range(self.n_inequiv_corr_shells)]
|
|
|
|
if self.symm_op:
|
|
#mpi.report("Do the init for symm:")
|
|
self.Symm_corr = Symmetry(hdf_file,subgroup=self.symm_corr_data)
|
|
|
|
# determine the smallest blocs, if wanted:
|
|
if (use_lda_blocks): dm=self.analyse_BS()
|
|
|
|
|
|
# now save things again to HDF5:
|
|
if (mpi.is_master_node()):
|
|
ar=HDFArchive(self.hdf_file,'a')
|
|
ar[self.lda_data]['h_field'] = self.h_field
|
|
del ar
|
|
self.save()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def read_input_from_hdf(self, subgrp, things_to_read, optional_things=[]):
|
|
"""
|
|
Reads data from the HDF file
|
|
"""
|
|
|
|
retval = True
|
|
# init variables on all nodes:
|
|
for it in things_to_read: exec "self.%s = 0"%it
|
|
for it in optional_things: exec "self.%s = 0"%it
|
|
|
|
if (mpi.is_master_node()):
|
|
ar=HDFArchive(self.hdf_file,'a')
|
|
if (subgrp in ar):
|
|
# first read the necessary things:
|
|
for it in things_to_read:
|
|
if (it in ar[subgrp]):
|
|
exec "self.%s = ar['%s']['%s']"%(it,subgrp,it)
|
|
else:
|
|
mpi.report("Loading %s failed!"%it)
|
|
retval = False
|
|
|
|
if ((retval) and (len(optional_things)>0)):
|
|
# if necessary things worked, now read optional things:
|
|
retval = {}
|
|
for it in optional_things:
|
|
if (it in ar[subgrp]):
|
|
exec "self.%s = ar['%s']['%s']"%(it,subgrp,it)
|
|
retval['%s'%it] = True
|
|
else:
|
|
retval['%s'%it] = False
|
|
else:
|
|
mpi.report("Loading failed: No %s subgroup in HDF5!"%subgrp)
|
|
retval = False
|
|
|
|
del ar
|
|
|
|
# now do the broadcasting:
|
|
for it in things_to_read: exec "self.%s = mpi.bcast(self.%s)"%(it,it)
|
|
for it in optional_things: exec "self.%s = mpi.bcast(self.%s)"%(it,it)
|
|
|
|
|
|
retval = mpi.bcast(retval)
|
|
|
|
return retval
|
|
|
|
|
|
|
|
def save(self):
|
|
"""Saves some quantities into an HDF5 arxiv"""
|
|
|
|
if not (mpi.is_master_node()): return # do nothing on nodes
|
|
|
|
ar=HDFArchive(self.hdf_file,'a')
|
|
ar[self.lda_data]['chemical_potential'] = self.chemical_potential
|
|
ar[self.lda_data]['dc_energ'] = self.dc_energ
|
|
ar[self.lda_data]['dc_imp'] = self.dc_imp
|
|
del ar
|
|
|
|
|
|
def load(self):
|
|
"""Loads some quantities from an HDF5 arxiv"""
|
|
|
|
things_to_read=['chemical_potential','dc_imp','dc_energ']
|
|
|
|
retval = self.read_input_from_hdf(subgrp=self.lda_data,things_to_read=things_to_read)
|
|
return retval
|
|
|
|
|
|
def downfold(self,ik,icrsh,sig,gf_to_downfold,gf_inp):
|
|
"""Downfolding a block of the Greens function"""
|
|
|
|
gf_downfolded = gf_inp.copy()
|
|
isp = self.names_to_ind[self.SO][sig] # get spin index for proj. matrices
|
|
dim = self.corr_shells[icrsh][3]
|
|
n_orb = self.n_orbitals[ik,isp]
|
|
|
|
gf_downfolded.from_L_G_R(self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb],gf_to_downfold,self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb].conjugate().transpose()) # downfolding G
|
|
|
|
return gf_downfolded
|
|
|
|
|
|
def upfold(self,ik,icrsh,sig,gf_to_upfold,gf_inp):
|
|
"""Upfolding a block of the Greens function"""
|
|
|
|
gf_upfolded = gf_inp.copy()
|
|
|
|
isp = self.names_to_ind[self.SO][sig] # get spin index for proj. matrices
|
|
dim = self.corr_shells[icrsh][3]
|
|
n_orb = self.n_orbitals[ik,isp]
|
|
|
|
gf_upfolded.from_L_G_R(self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb].conjugate().transpose(),gf_to_upfold,self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb])
|
|
|
|
return gf_upfolded
|
|
|
|
|
|
def rotloc(self,icrsh,gf_to_rotate,direction):
|
|
"""Local <-> Global rotation of a GF block.
|
|
direction: 'toLocal' / 'toGlobal' """
|
|
|
|
assert ((direction=='toLocal')or(direction=='toGlobal')),"Give direction 'toLocal' or 'toGlobal' in rotloc!"
|
|
|
|
gf_rotated = gf_to_rotate.copy()
|
|
if (direction=='toGlobal'):
|
|
#if (self.rot_mat_time_inv[icrsh]==1): gf_rotated <<= gf_rotated.transpose()
|
|
#gf_rotated.from_L_G_R(self.rot_mat[icrsh].transpose(),gf_rotated,self.rot_mat[icrsh].conjugate())
|
|
if ((self.rot_mat_time_inv[icrsh]==1) and (self.SO)):
|
|
gf_rotated <<= gf_rotated.transpose()
|
|
gf_rotated.from_L_G_R(self.rot_mat[icrsh].conjugate(),gf_rotated,self.rot_mat[icrsh].transpose())
|
|
else:
|
|
gf_rotated.from_L_G_R(self.rot_mat[icrsh],gf_rotated,self.rot_mat[icrsh].conjugate().transpose())
|
|
|
|
elif (direction=='toLocal'):
|
|
if ((self.rot_mat_time_inv[icrsh]==1)and(self.SO)):
|
|
gf_rotated <<= gf_rotated.transpose()
|
|
gf_rotated.from_L_G_R(self.rot_mat[icrsh].transpose(),gf_rotated,self.rot_mat[icrsh].conjugate())
|
|
else:
|
|
gf_rotated.from_L_G_R(self.rot_mat[icrsh].conjugate().transpose(),gf_rotated,self.rot_mat[icrsh])
|
|
|
|
return gf_rotated
|
|
|
|
|
|
def lattice_gf_matsubara(self,ik,mu,beta=40,with_Sigma=True):
|
|
"""Calculates the lattice Green function from the LDA hopping and the self energy at k-point number ik
|
|
and chemical potential mu."""
|
|
|
|
ntoi = self.names_to_ind[self.SO]
|
|
bln = self.block_names[self.SO]
|
|
|
|
if (not hasattr(self,"Sigma_imp")): with_Sigma=False
|
|
|
|
if (with_Sigma):
|
|
stmp = self.add_dc()
|
|
beta = self.Sigma_imp[0].mesh.beta #override beta if Sigma is present
|
|
|
|
if (self.Gupf is None):
|
|
# first setting up of Gupf
|
|
BS = [ range(self.n_orbitals[ik,ntoi[ib]]) for ib in bln ]
|
|
gf_struct = [ (bln[ib], BS[ib]) for ib in range(self.n_spin_blocks_gf[self.SO]) ]
|
|
a_list = [a for a,al in gf_struct]
|
|
if (with_Sigma): #take the mesh from Sigma if necessary
|
|
glist = lambda : [ GfImFreq(indices = al, mesh = self.Sigma_imp[0].mesh) for a,al in gf_struct]
|
|
else:
|
|
glist = lambda : [ GfImFreq(indices = al, beta = beta) for a,al in gf_struct]
|
|
self.Gupf = BlockGf(name_list = a_list, block_list = glist(),make_copies=False)
|
|
self.Gupf.zero()
|
|
self.Gupf_id = self.Gupf.copy()
|
|
self.Gupf_id <<= iOmega_n
|
|
|
|
GFsize = [ gf.N1 for sig,gf in self.Gupf]
|
|
unchangedsize = all( [ self.n_orbitals[ik,ntoi[bln[ib]]]==GFsize[ib]
|
|
for ib in range(self.n_spin_blocks_gf[self.SO]) ] )
|
|
|
|
if ((not unchangedsize)or(self.Gupf.mesh.beta!=beta)):
|
|
BS = [ range(self.n_orbitals[ik,ntoi[ib]]) for ib in bln ]
|
|
gf_struct = [ (bln[ib], BS[ib]) for ib in range(self.n_spin_blocks_gf[self.SO]) ]
|
|
a_list = [a for a,al in gf_struct]
|
|
if (with_Sigma):
|
|
glist = lambda : [ GfImFreq(indices = al, mesh = self.Sigma_imp[0].mesh) for a,al in gf_struct]
|
|
else:
|
|
glist = lambda : [ GfImFreq(indices = al, beta = beta) for a,al in gf_struct]
|
|
self.Gupf = BlockGf(name_list = a_list, block_list = glist(),make_copies=False)
|
|
self.Gupf.zero()
|
|
self.Gupf_id = self.Gupf.copy()
|
|
self.Gupf_id <<= iOmega_n
|
|
|
|
|
|
idmat = [numpy.identity(self.n_orbitals[ik,ntoi[bl]],numpy.complex_) for bl in bln]
|
|
#for ibl in range(self.n_spin_blocks_gf[self.SO]): mupat[ibl] *= mu
|
|
|
|
self.Gupf <<= self.Gupf_id
|
|
M = copy.deepcopy(idmat)
|
|
for ibl in range(self.n_spin_blocks_gf[self.SO]):
|
|
ind = ntoi[bln[ibl]]
|
|
n_orb = self.n_orbitals[ik,ind]
|
|
M[ibl] = self.hopping[ik,ind,0:n_orb,0:n_orb] - (idmat[ibl]*mu) - (idmat[ibl] * self.h_field * (1-2*ibl))
|
|
self.Gupf -= M
|
|
|
|
if (with_Sigma):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for sig,gf in self.Gupf: gf -= self.upfold(ik,icrsh,sig,stmp[icrsh][sig],gf)
|
|
|
|
self.Gupf.invert()
|
|
|
|
return self.Gupf
|
|
|
|
|
|
def check_projectors(self):
|
|
|
|
dens_mat = [numpy.zeros([self.corr_shells[ish][3],self.corr_shells[ish][3]],numpy.complex_)
|
|
for ish in range(self.n_corr_shells)]
|
|
|
|
for ik in range(self.n_k):
|
|
|
|
for ish in range(self.n_corr_shells):
|
|
dim = self.corr_shells[ish][3]
|
|
n_orb = self.n_orbitals[ik,0]
|
|
dens_mat[ish][:,:] += numpy.dot(self.proj_mat[ik,0,ish,0:dim,0:n_orb],self.proj_mat[ik,0,ish,0:dim,0:n_orb].transpose().conjugate()) * self.bz_weights[ik]
|
|
|
|
if (self.symm_op!=0): dens_mat = self.Symm_corr.symmetrize(dens_mat)
|
|
|
|
# Rotate to local coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
if (self.rot_mat_time_inv[icrsh]==1): dens_mat[icrsh] = dens_mat[icrsh].conjugate()
|
|
dens_mat[icrsh] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh]) ,
|
|
self.rot_mat[icrsh] )
|
|
|
|
|
|
return dens_mat
|
|
|
|
|
|
|
|
def simple_point_dens_mat(self):
|
|
|
|
|
|
ntoi = self.names_to_ind[self.SO]
|
|
bln = self.block_names[self.SO]
|
|
|
|
MMat = [numpy.zeros( [self.n_orbitals[0,ntoi[bl]],self.n_orbitals[0,ntoi[bl]]], numpy.complex_) for bl in bln]
|
|
|
|
dens_mat = [ {} for icrsh in xrange(self.n_corr_shells)]
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bl in self.block_names[self.corr_shells[icrsh][4]]:
|
|
dens_mat[icrsh][bl] = numpy.zeros([self.corr_shells[icrsh][3],self.corr_shells[icrsh][3]], numpy.complex_)
|
|
|
|
ikarray=numpy.array(range(self.n_k))
|
|
|
|
for ik in mpi.slice_array(ikarray):
|
|
|
|
unchangedsize = all( [ self.n_orbitals[ik,ntoi[bln[ib]]]==len(MMat[ib])
|
|
for ib in range(self.n_spin_blocks_gf[self.SO]) ] )
|
|
|
|
if (not unchangedsize):
|
|
MMat = [numpy.zeros( [self.n_orbitals[ik,ntoi[bl]],self.n_orbitals[ik,ntoi[bl]]], numpy.complex_) for bl in bln]
|
|
|
|
for ibl,bl in enumerate(bln):
|
|
ind = ntoi[bl]
|
|
for inu in range(self.n_orbitals[ik,ind]):
|
|
if ( (self.hopping[ik,ind,inu,inu]-self.h_field*(1-2*ibl)) < 0.0):
|
|
MMat[ibl][inu,inu] = 1.0
|
|
else:
|
|
MMat[ibl][inu,inu] = 0.0
|
|
|
|
|
|
for icrsh in range(self.n_corr_shells):
|
|
for ibn,bn in enumerate(self.block_names[self.corr_shells[icrsh][4]]):
|
|
isp = self.names_to_ind[self.corr_shells[icrsh][4]][bn]
|
|
dim = self.corr_shells[icrsh][3]
|
|
n_orb = self.n_orbitals[ik,isp]
|
|
|
|
#print ik, bn, isp
|
|
dens_mat[icrsh][bn] += self.bz_weights[ik] * numpy.dot( numpy.dot(self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb],MMat[ibn]) ,
|
|
self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb].transpose().conjugate() )
|
|
|
|
# get data from nodes:
|
|
for icrsh in range(self.n_corr_shells):
|
|
for sig in dens_mat[icrsh]:
|
|
dens_mat[icrsh][sig] = mpi.all_reduce(mpi.world,dens_mat[icrsh][sig],lambda x,y : x+y)
|
|
mpi.barrier()
|
|
|
|
|
|
if (self.symm_op!=0): dens_mat = self.Symm_corr.symmetrize(dens_mat)
|
|
|
|
# Rotate to local coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bn in dens_mat[icrsh]:
|
|
if (self.rot_mat_time_inv[icrsh]==1): dens_mat[icrsh][bn] = dens_mat[icrsh][bn].conjugate()
|
|
dens_mat[icrsh][bn] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh][bn]) ,
|
|
self.rot_mat[icrsh])
|
|
|
|
|
|
return dens_mat
|
|
|
|
|
|
def density_gf(self,beta):
|
|
"""Calculates the density without setting up Gloc. It is useful for Hubbard I, and very fast."""
|
|
|
|
dens_mat = [ {} for icrsh in xrange(self.n_corr_shells)]
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bl in self.block_names[self.corr_shells[icrsh][4]]:
|
|
dens_mat[icrsh][bl] = numpy.zeros([self.corr_shells[icrsh][3],self.corr_shells[icrsh][3]], numpy.complex_)
|
|
|
|
ikarray=numpy.array(range(self.n_k))
|
|
|
|
for ik in mpi.slice_array(ikarray):
|
|
|
|
Gupf = self.lattice_gf_matsubara(ik=ik, beta=beta, mu=self.chemical_potential)
|
|
Gupf *= self.bz_weights[ik]
|
|
dm = Gupf.density()
|
|
MMat = [dm[bl] for bl in self.block_names[self.SO]]
|
|
|
|
for icrsh in range(self.n_corr_shells):
|
|
for ibn,bn in enumerate(self.block_names[self.corr_shells[icrsh][4]]):
|
|
isp = self.names_to_ind[self.corr_shells[icrsh][4]][bn]
|
|
dim = self.corr_shells[icrsh][3]
|
|
n_orb = self.n_orbitals[ik,isp]
|
|
#print ik, bn, isp
|
|
dens_mat[icrsh][bn] += numpy.dot( numpy.dot(self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb],MMat[ibn]),
|
|
self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb].transpose().conjugate() )
|
|
|
|
# get data from nodes:
|
|
for icrsh in range(self.n_corr_shells):
|
|
for sig in dens_mat[icrsh]:
|
|
dens_mat[icrsh][sig] = mpi.all_reduce(mpi.world,dens_mat[icrsh][sig],lambda x,y : x+y)
|
|
mpi.barrier()
|
|
|
|
|
|
if (self.symm_op!=0): dens_mat = self.Symm_corr.symmetrize(dens_mat)
|
|
|
|
# Rotate to local coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bn in dens_mat[icrsh]:
|
|
if (self.rot_mat_time_inv[icrsh]==1): dens_mat[icrsh][bn] = dens_mat[icrsh][bn].conjugate()
|
|
dens_mat[icrsh][bn] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh][bn]) ,
|
|
self.rot_mat[icrsh] )
|
|
|
|
return dens_mat
|
|
|
|
|
|
|
|
def analyse_BS(self, threshold = 0.00001, include_shells = None, dm = None):
|
|
""" Determines the Greens function block structure from the simple point integration"""
|
|
|
|
if (dm==None): dm = self.simple_point_dens_mat()
|
|
|
|
dens_mat = [dm[self.invshellmap[ish]] for ish in xrange(self.n_inequiv_corr_shells) ]
|
|
|
|
if include_shells is None: include_shells=range(self.n_inequiv_corr_shells)
|
|
for ish in include_shells:
|
|
|
|
#self.gf_struct_solver.append([])
|
|
self.gf_struct_solver[ish] = []
|
|
gf_struct_temp = []
|
|
|
|
a_list = [a for a,al in self.gf_struct_corr[self.invshellmap[ish]] ]
|
|
for a in a_list:
|
|
|
|
dm = dens_mat[ish][a]
|
|
dmbool = (abs(dm) > threshold) # gives an index list of entries larger that threshold
|
|
|
|
offdiag = []
|
|
for i in xrange(len(dmbool)):
|
|
for j in xrange(i,len(dmbool)):
|
|
if ((dmbool[i,j])&(i!=j)): offdiag.append([i,j])
|
|
|
|
NBlocs = len(dmbool)
|
|
blocs = [ [i] for i in range(NBlocs) ]
|
|
|
|
for i in range(len(offdiag)):
|
|
if (offdiag[i][0]!=offdiag[i][1]):
|
|
for j in range(len(blocs[offdiag[i][1]])): blocs[offdiag[i][0]].append(blocs[offdiag[i][1]][j])
|
|
del blocs[offdiag[i][1]]
|
|
for j in range(i+1,len(offdiag)):
|
|
if (offdiag[j][0]==offdiag[i][1]): offdiag[j][0]=offdiag[i][0]
|
|
if (offdiag[j][1]==offdiag[i][1]): offdiag[j][1]=offdiag[i][0]
|
|
if (offdiag[j][0]>offdiag[i][1]): offdiag[j][0] -= 1
|
|
if (offdiag[j][1]>offdiag[i][1]): offdiag[j][1] -= 1
|
|
offdiag[j].sort()
|
|
NBlocs-=1
|
|
|
|
for i in range(NBlocs):
|
|
blocs[i].sort()
|
|
self.gf_struct_solver[ish].append( ('%s%s'%(a,i),range(len(blocs[i]))) )
|
|
gf_struct_temp.append( ('%s%s'%(a,i),blocs[i]) )
|
|
|
|
|
|
# map is the mapping of the blocs from the SK blocs to the CTQMC blocs:
|
|
self.map[ish][a] = range(len(dmbool))
|
|
for ibl in range(NBlocs):
|
|
for j in range(len(blocs[ibl])):
|
|
self.map[ish][a][blocs[ibl][j]] = '%s%s'%(a,ibl)
|
|
self.map_inv[ish]['%s%s'%(a,ibl)] = a
|
|
|
|
|
|
# now calculate degeneracies of orbitals:
|
|
dm = {}
|
|
for bl in gf_struct_temp:
|
|
bln = bl[0]
|
|
ind = bl[1]
|
|
# get dm for the blocks:
|
|
dm[bln] = numpy.zeros([len(ind),len(ind)],numpy.complex_)
|
|
for i in range(len(ind)):
|
|
for j in range(len(ind)):
|
|
dm[bln][i,j] = dens_mat[ish][self.map_inv[ish][bln]][ind[i],ind[j]]
|
|
|
|
for bl in gf_struct_temp:
|
|
for bl2 in gf_struct_temp:
|
|
if (dm[bl[0]].shape==dm[bl2[0]].shape) :
|
|
if ( ( (abs(dm[bl[0]]-dm[bl2[0]])<threshold).all() ) and (bl[0]!=bl2[0]) ):
|
|
# check if it was already there:
|
|
ind1=-1
|
|
ind2=-2
|
|
for n,ind in enumerate(self.deg_shells[ish]):
|
|
if (bl[0] in ind): ind1=n
|
|
if (bl2[0] in ind): ind2=n
|
|
if ((ind1<0)and(ind2>=0)):
|
|
self.deg_shells[ish][ind2].append(bl[0])
|
|
elif ((ind1>=0)and(ind2<0)):
|
|
self.deg_shells[ish][ind1].append(bl2[0])
|
|
elif ((ind1<0)and(ind2<0)):
|
|
self.deg_shells[ish].append([bl[0],bl2[0]])
|
|
|
|
if (mpi.is_master_node()):
|
|
ar=HDFArchive(self.hdf_file,'a')
|
|
ar[self.lda_data]['gf_struct_solver'] = self.gf_struct_solver
|
|
ar[self.lda_data]['map'] = self.map
|
|
ar[self.lda_data]['map_inv'] = self.map_inv
|
|
try:
|
|
ar[self.lda_data]['deg_shells'] = self.deg_shells
|
|
except:
|
|
mpi.report("deg_shells not stored, degeneracies not found")
|
|
del ar
|
|
|
|
return dens_mat
|
|
|
|
|
|
def symm_deg_gf(self,gf_to_symm,orb):
|
|
"""Symmetrises a GF for the given degenerate shells self.deg_shells"""
|
|
|
|
for degsh in self.deg_shells[orb]:
|
|
#loop over degenerate shells:
|
|
ss = gf_to_symm[degsh[0]].copy()
|
|
ss.zero()
|
|
Ndeg = len(degsh)
|
|
for bl in degsh: ss += gf_to_symm[bl] / (1.0*Ndeg)
|
|
for bl in degsh: gf_to_symm[bl] <<= ss
|
|
|
|
|
|
def eff_atomic_levels(self):
|
|
"""Calculates the effective atomic levels needed as input for the Hubbard I Solver."""
|
|
|
|
# define matrices for inequivalent shells:
|
|
eff_atlevels = [ {} for ish in range(self.n_inequiv_corr_shells) ]
|
|
for ish in range(self.n_inequiv_corr_shells):
|
|
for bn in self.block_names[self.corr_shells[self.invshellmap[ish]][4]]:
|
|
eff_atlevels[ish][bn] = numpy.identity(self.corr_shells[self.invshellmap[ish]][3], numpy.complex_)
|
|
|
|
# Chemical Potential:
|
|
for ish in xrange(self.n_inequiv_corr_shells):
|
|
for ii in eff_atlevels[ish]: eff_atlevels[ish][ii] *= -self.chemical_potential
|
|
|
|
# double counting term:
|
|
#if hasattr(self,"dc_imp"):
|
|
for ish in xrange(self.n_inequiv_corr_shells):
|
|
for ii in eff_atlevels[ish]:
|
|
eff_atlevels[ish][ii] -= self.dc_imp[self.invshellmap[ish]][ii]
|
|
|
|
# sum over k:
|
|
if not hasattr(self,"Hsumk"):
|
|
# calculate the sum over k. Does not depend on mu, so do it only once:
|
|
self.Hsumk = [ {} for ish in range(self.n_corr_shells) ]
|
|
for icrsh in range(self.n_corr_shells):
|
|
for bn in self.block_names[self.corr_shells[icrsh][4]]:
|
|
dim = self.corr_shells[icrsh][3] #*(1+self.corr_shells[icrsh][4])
|
|
self.Hsumk[icrsh][bn] = numpy.zeros([dim,dim],numpy.complex_)
|
|
|
|
for icrsh in range(self.n_corr_shells):
|
|
dim = self.corr_shells[icrsh][3]
|
|
for ibn, bn in enumerate(self.block_names[self.corr_shells[icrsh][4]]):
|
|
isp = self.names_to_ind[self.corr_shells[icrsh][4]][bn]
|
|
for ik in xrange(self.n_k):
|
|
n_orb = self.n_orbitals[ik,isp]
|
|
MMat = numpy.identity(n_orb, numpy.complex_)
|
|
MMat = self.hopping[ik,isp,0:n_orb,0:n_orb] - (1-2*ibn) * self.h_field * MMat
|
|
self.Hsumk[icrsh][bn] += self.bz_weights[ik] * numpy.dot( numpy.dot(self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb],MMat), #self.hopping[ik][isp]) ,
|
|
self.proj_mat[ik,isp,icrsh,0:dim,0:n_orb].conjugate().transpose() )
|
|
|
|
# symmetrisation:
|
|
if (self.symm_op!=0): self.Hsumk = self.Symm_corr.symmetrize(self.Hsumk)
|
|
|
|
# Rotate to local coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bn in self.Hsumk[icrsh]:
|
|
|
|
if (self.rot_mat_time_inv[icrsh]==1): self.Hsumk[icrsh][bn] = self.Hsumk[icrsh][bn].conjugate()
|
|
#if (self.corr_shells[icrsh][4]==0): self.Hsumk[icrsh][bn] = self.Hsumk[icrsh][bn].conjugate()
|
|
|
|
self.Hsumk[icrsh][bn] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),self.Hsumk[icrsh][bn]) ,
|
|
self.rot_mat[icrsh] )
|
|
|
|
# add to matrix:
|
|
for ish in xrange(self.n_inequiv_corr_shells):
|
|
for bn in eff_atlevels[ish]:
|
|
eff_atlevels[ish][bn] += self.Hsumk[self.invshellmap[ish]][bn]
|
|
|
|
|
|
return eff_atlevels
|
|
|
|
|
|
|
|
def __init_dc(self):
|
|
|
|
# construct the density matrix dm_imp and double counting arrays
|
|
#self.dm_imp = [ {} for i in xrange(self.n_corr_shells)]
|
|
self.dc_imp = [ {} for i in xrange(self.n_corr_shells)]
|
|
for i in xrange(self.n_corr_shells):
|
|
l = self.corr_shells[i][3]
|
|
for j in xrange(len(self.gf_struct_corr[i])):
|
|
self.dc_imp[i]['%s'%self.gf_struct_corr[i][j][0]] = numpy.zeros([l,l],numpy.float_)
|
|
self.dc_energ = [0.0 for i in xrange(self.n_corr_shells)]
|
|
|
|
|
|
|
|
def set_lichtenstein_dc(self,Sigma_imp):
|
|
"""Sets a double counting term according to Lichtenstein et al. PRL2001"""
|
|
|
|
assert 0,"Lichtenstein DC not supported any more!"
|
|
|
|
|
|
|
|
|
|
def set_dc(self,dens_mat,U_interact,J_hund,orb=0,use_dc_formula=0,use_val=None):
|
|
"""Sets the double counting term for inequiv orbital orb
|
|
use_dc_formula=0: LDA+U FLL double counting, use_dc_formula=1: Held's formula.
|
|
use_dc_formula=2: AMF
|
|
Be sure that you use the correct interaction Hamiltonian!"""
|
|
|
|
|
|
#if (not hasattr(self,"dc_imp")): self.__init_dc()
|
|
|
|
|
|
#dm = [ {} for i in xrange(self.n_corr_shells)]
|
|
#for i in xrange(self.n_corr_shells):
|
|
# l = self.corr_shells[i][3] #*(1+self.corr_shells[i][4])
|
|
# for j in xrange(len(self.gf_struct_corr[i])):
|
|
# dm[i]['%s'%self.gf_struct_corr[i][j][0]] = numpy.zeros([l,l],numpy.float_)
|
|
|
|
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
|
|
iorb = self.shellmap[icrsh] # iorb is the index of the inequivalent shell corresponding to icrsh
|
|
|
|
if (iorb==orb):
|
|
# do this orbital
|
|
Ncr = {}
|
|
l = self.corr_shells[icrsh][3] #*(1+self.corr_shells[icrsh][4])
|
|
|
|
for j in xrange(len(self.gf_struct_corr[icrsh])):
|
|
self.dc_imp[icrsh]['%s'%self.gf_struct_corr[icrsh][j][0]] = numpy.identity(l,numpy.float_)
|
|
blname = self.gf_struct_corr[icrsh][j][0]
|
|
Ncr[blname] = 0.0
|
|
|
|
for a,al in self.gf_struct_solver[iorb]:
|
|
#for bl in self.map[iorb][blname]:
|
|
bl = self.map_inv[iorb][a]
|
|
#print 'bl, valiue = ',bl,dens_mat[a].real.trace()
|
|
Ncr[bl] += dens_mat[a].real.trace()
|
|
|
|
#print 'Ncr=',Ncr
|
|
M = self.corr_shells[icrsh][3]
|
|
|
|
Ncrtot = 0.0
|
|
a_list = [a for a,al in self.gf_struct_corr[icrsh]]
|
|
for bl in a_list:
|
|
Ncrtot += Ncr[bl]
|
|
|
|
# average the densities if there is no SP:
|
|
if (self.SP==0):
|
|
for bl in a_list:
|
|
Ncr[bl] = Ncrtot / len(a_list)
|
|
# correction for SO: we have only one block in this case, but in DC we need N/2
|
|
elif (self.SP==1 and self.SO==1):
|
|
for bl in a_list:
|
|
Ncr[bl] = Ncrtot / 2.0
|
|
|
|
if (use_val is None):
|
|
|
|
if (use_dc_formula==0):
|
|
self.dc_energ[icrsh] = U_interact / 2.0 * Ncrtot * (Ncrtot-1.0)
|
|
for bl in a_list:
|
|
Uav = U_interact*(Ncrtot-0.5) - J_hund*(Ncr[bl] - 0.5)
|
|
self.dc_imp[icrsh][bl] *= Uav
|
|
self.dc_energ[icrsh] -= J_hund / 2.0 * (Ncr[bl]) * (Ncr[bl]-1.0)
|
|
mpi.report("DC for shell %(icrsh)i and block %(bl)s = %(Uav)f"%locals())
|
|
elif (use_dc_formula==1):
|
|
self.dc_energ[icrsh] = (U_interact + (M-1)*(U_interact-2.0*J_hund) + (M-1)*(U_interact-3.0*J_hund))/(2*M-1) / 2.0 * Ncrtot * (Ncrtot-1.0)
|
|
#self.dc_energ[icrsh] = (U_interact + J_hund * (2.0-(M-1)) / (2*M-1) ) / 2.0 * Ncrtot * (Ncrtot-1.0)
|
|
for bl in a_list:
|
|
# Held's formula, with U_interact the interorbital onsite interaction
|
|
Uav =(U_interact + (M-1)*(U_interact-2.0*J_hund) + (M-1)*(U_interact-3.0*J_hund))/(2*M-1) * (Ncrtot-0.5)
|
|
#Uav = (U_interact + J_hund * (2.0-(M-1)) / (2*M-1) ) * (Ncrtot-0.5)
|
|
self.dc_imp[icrsh][bl] *= Uav
|
|
mpi.report("DC for shell %(icrsh)i and block %(bl)s = %(Uav)f"%locals())
|
|
elif (use_dc_formula==2):
|
|
self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
|
|
for bl in a_list:
|
|
# AMF
|
|
Uav = U_interact*(Ncrtot - Ncr[bl]/M) - J_hund * (Ncr[bl] - Ncr[bl]/M)
|
|
self.dc_imp[icrsh][bl] *= Uav
|
|
self.dc_energ[icrsh] -= (U_interact + (M-1)*J_hund)/M * 0.5 * Ncr[bl] * Ncr[bl]
|
|
mpi.report("DC for shell %(icrsh)i and block %(bl)s = %(Uav)f"%locals())
|
|
|
|
# output:
|
|
mpi.report("DC energy for shell %s = %s"%(icrsh,self.dc_energ[icrsh]))
|
|
|
|
else:
|
|
|
|
a_list = [a for a,al in self.gf_struct_corr[icrsh]]
|
|
for bl in a_list:
|
|
self.dc_imp[icrsh][bl] *= use_val
|
|
|
|
self.dc_energ[icrsh] = use_val * Ncrtot
|
|
|
|
# output:
|
|
mpi.report("DC for shell %(icrsh)i = %(use_val)f"%locals())
|
|
mpi.report("DC energy = %s"%self.dc_energ[icrsh])
|
|
|
|
|
|
|
|
|
|
|
|
def find_dc(self,orb,guess,dens_mat,dens_req=None,precision=0.01):
|
|
"""searches for DC in order to fulfill charge neutrality.
|
|
If dens_req is given, then DC is set such that the LOCAL charge of orbital
|
|
orb coincides with dens_req."""
|
|
|
|
mu = self.chemical_potential
|
|
|
|
def F(dc):
|
|
self.set_dc(dens_mat=dens_mat,U_interact=0,J_hund=0,orb=orb,use_val=dc)
|
|
if (dens_req is None):
|
|
return self.total_density(mu=mu)
|
|
else:
|
|
return self.extract_G_loc()[orb].total_density()
|
|
|
|
|
|
if (dens_req is None):
|
|
Dens_rel = self.density_required - self.charge_below
|
|
else:
|
|
Dens_rel = dens_req
|
|
|
|
dcnew = dichotomy.dichotomy(function = F,
|
|
x_init = guess, y_value = Dens_rel,
|
|
precision_on_y = precision, delta_x=0.5,
|
|
max_loops = 100, x_name="Double-Counting", y_name= "Total Density",
|
|
verbosity = 3)[0]
|
|
|
|
return dcnew
|
|
|
|
|
|
|
|
|
|
|
|
def put_Sigma(self, Sigma_imp):
|
|
"""Puts the impurity self energies for inequivalent atoms into the class, respects the multiplicity of the atoms."""
|
|
|
|
assert isinstance(Sigma_imp,list), "Sigma_imp has to be a list of Sigmas for the correlated shells, even if it is of length 1!"
|
|
assert len(Sigma_imp)==self.n_inequiv_corr_shells, "give exactly one Sigma for each inequivalent corr. shell!"
|
|
|
|
|
|
# init self.Sigma_imp:
|
|
if Sigma_imp[0].note == 'ReFreq':
|
|
# Real frequency Sigma:
|
|
self.Sigma_imp = [ BlockGf( name_block_generator = [ (a,GfReFreq(indices = al, mesh = Sigma_imp[0].mesh)) for a,al in self.gf_struct_corr[i] ],
|
|
make_copies = False) for i in xrange(self.n_corr_shells) ]
|
|
for i in xrange(self.n_corr_shells): self.Sigma_imp[i].note='ReFreq'
|
|
else:
|
|
# Imaginary frequency Sigma:
|
|
self.Sigma_imp = [ BlockGf( name_block_generator = [ (a,GfImFreq(indices = al, mesh = Sigma_imp[0].mesh)) for a,al in self.gf_struct_corr[i] ],
|
|
make_copies = False) for i in xrange(self.n_corr_shells) ]
|
|
|
|
# transform the CTQMC blocks to the full matrix:
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
s = self.shellmap[icrsh] # s is the index of the inequivalent shell corresponding to icrsh
|
|
|
|
# setting up the index map:
|
|
map_ind={}
|
|
cnt = {}
|
|
for blname in self.map[s]:
|
|
cnt[blname] = 0
|
|
|
|
for a,al in self.gf_struct_solver[s]:
|
|
blname = self.map_inv[s][a]
|
|
map_ind[a] = range(len(al))
|
|
for i in al:
|
|
map_ind[a][i] = cnt[blname]
|
|
cnt[blname]+=1
|
|
|
|
|
|
for ibl in range(len(self.gf_struct_solver[s])):
|
|
for i in range(len(self.gf_struct_solver[s][ibl][1])):
|
|
for j in range(len(self.gf_struct_solver[s][ibl][1])):
|
|
bl = self.gf_struct_solver[s][ibl][0]
|
|
ind1 = self.gf_struct_solver[s][ibl][1][i]
|
|
ind2 = self.gf_struct_solver[s][ibl][1][j]
|
|
ind1_imp = map_ind[bl][ind1]
|
|
ind2_imp = map_ind[bl][ind2]
|
|
self.Sigma_imp[icrsh][self.map_inv[s][bl]][ind1_imp,ind2_imp] <<= Sigma_imp[s][bl][ind1,ind2]
|
|
|
|
# rotation from local to global coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for sig,gf in self.Sigma_imp[icrsh]: self.Sigma_imp[icrsh][sig] <<= self.rotloc(icrsh,gf,direction='toGlobal')
|
|
|
|
|
|
|
|
def add_dc(self):
|
|
"""Substracts the double counting term from the impurity self energy."""
|
|
|
|
# Be careful: Sigma_imp is already in the global coordinate system!!
|
|
sres = [s.copy() for s in self.Sigma_imp]
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for bl,gf in sres[icrsh]:
|
|
dccont = numpy.dot(self.rot_mat[icrsh],numpy.dot(self.dc_imp[icrsh][bl],self.rot_mat[icrsh].conjugate().transpose()))
|
|
sres[icrsh][bl] -= dccont
|
|
|
|
return sres
|
|
|
|
|
|
|
|
def set_mu(self,mu):
|
|
"""Sets a new chemical potential"""
|
|
self.chemical_potential = mu
|
|
#print "Chemical potential in SumK set to ",mu
|
|
|
|
|
|
|
|
def sorts_of_atoms(self,lst):
|
|
"""
|
|
This routine should determine the number of sorts in the double list lst
|
|
"""
|
|
sortlst = [ lst[i][1] for i in xrange(len(lst)) ]
|
|
sortlst.sort()
|
|
sorts = 1
|
|
for i in xrange(len(sortlst)-1):
|
|
if sortlst[i+1]>sortlst[i]: sorts += 1
|
|
|
|
return sorts
|
|
|
|
|
|
|
|
def number_of_atoms(self,lst):
|
|
"""
|
|
This routine should determine the number of atoms in the double list lst
|
|
"""
|
|
atomlst = [ lst[i][0] for i in xrange(len(lst)) ]
|
|
atomlst.sort()
|
|
atoms = 1
|
|
for i in xrange(len(atomlst)-1):
|
|
if atomlst[i+1]>atomlst[i]: atoms += 1
|
|
|
|
return atoms
|
|
|
|
|
|
|
|
def inequiv_shells(self,lst):
|
|
"""
|
|
The number of inequivalent shells is calculated from lst, and a mapping is given as
|
|
map(i_corr_shells) = i_inequiv_corr_shells
|
|
invmap(i_inequiv_corr_shells) = i_corr_shells
|
|
in order to put the Self energies to all equivalent shells, and for extracting Gloc
|
|
"""
|
|
|
|
tmp = []
|
|
self.shellmap = [0 for i in range(len(lst))]
|
|
self.invshellmap = [0]
|
|
self.n_inequiv_corr_shells = 1
|
|
tmp.append( lst[0][1:3] )
|
|
|
|
if (len(lst)>1):
|
|
for i in range(len(lst)-1):
|
|
|
|
fnd = False
|
|
for j in range(self.n_inequiv_corr_shells):
|
|
if (tmp[j]==lst[i+1][1:3]):
|
|
fnd = True
|
|
self.shellmap[i+1] = j
|
|
if (fnd==False):
|
|
self.shellmap[i+1] = self.n_inequiv_corr_shells
|
|
self.n_inequiv_corr_shells += 1
|
|
tmp.append( lst[i+1][1:3] )
|
|
self.invshellmap.append(i+1)
|
|
|
|
|
|
|
|
def total_density(self, mu):
|
|
"""
|
|
Calculates the total charge for the energy window for a given mu. Since in general n_orbitals depends on k,
|
|
the calculation is done in the following order:
|
|
G_aa'(k,iw) -> n(k) = Tr G_aa'(k,iw) -> sum_k n_k
|
|
|
|
mu: chemical potential
|
|
|
|
The calculation is done in the global coordinate system, if distinction is made between local/global!
|
|
"""
|
|
|
|
dens = 0.0
|
|
ikarray=numpy.array(range(self.n_k))
|
|
|
|
for ik in mpi.slice_array(ikarray):
|
|
|
|
S = self.lattice_gf_matsubara(ik=ik,mu=mu)
|
|
dens += self.bz_weights[ik] * S.total_density()
|
|
|
|
# collect data from mpi:
|
|
dens = mpi.all_reduce(mpi.world,dens,lambda x,y : x+y)
|
|
mpi.barrier()
|
|
|
|
return dens
|
|
|
|
|
|
def find_mu(self, precision = 0.01):
|
|
"""Searches for mu in order to give the desired charge
|
|
A desired precision can be specified in precision."""
|
|
|
|
F = lambda mu : self.total_density(mu = mu)
|
|
|
|
Dens_rel = self.density_required - self.charge_below
|
|
|
|
|
|
self.chemical_potential = dichotomy.dichotomy(function = F,
|
|
x_init = self.chemical_potential, y_value = Dens_rel,
|
|
precision_on_y = precision, delta_x=0.5,
|
|
max_loops = 100, x_name="chemical_potential", y_name= "Total Density",
|
|
verbosity = 3)[0]
|
|
|
|
return self.chemical_potential
|
|
|
|
|
|
|
|
def find_mu_nonint(self, dens_req, orb = None, beta = 40, precision = 0.01):
|
|
|
|
def F(mu):
|
|
#gnonint = self.nonint_G(beta=beta,mu=mu)
|
|
gnonint = self.extract_G_loc(mu=mu,with_Sigma=False)
|
|
|
|
if (orb is None):
|
|
dens = 0.0
|
|
for ish in range(self.n_inequiv_corr_shells):
|
|
dens += gnonint[ish].total_density()
|
|
else:
|
|
dens = gnonint[orb].total_density()
|
|
|
|
return dens
|
|
|
|
|
|
self.chemical_potential = dichotomy.dichotomy(function = F,
|
|
x_init = self.chemical_potential, y_value = dens_req,
|
|
precision_on_y = precision, delta_x=0.5,
|
|
max_loops = 100, x_name="chemical_potential", y_name= "Local Density",
|
|
verbosity = 3)[0]
|
|
|
|
return self.chemical_potential
|
|
|
|
|
|
|
|
def extract_G_loc(self, mu=None, with_Sigma = True):
|
|
"""
|
|
extracts the local downfolded Green function at the chemical potential of the class.
|
|
At the end, the local G is rotated from the gloabl coordinate system to the local system.
|
|
if with_Sigma = False: Sigma is not included => non-interacting local GF
|
|
"""
|
|
|
|
if (mu is None): mu = self.chemical_potential
|
|
|
|
Gloc = [ self.Sigma_imp[icrsh].copy() for icrsh in xrange(self.n_corr_shells) ] # this list will be returned
|
|
for icrsh in xrange(self.n_corr_shells): Gloc[icrsh].zero() # initialize to zero
|
|
beta = Gloc[0].mesh.beta
|
|
|
|
ikarray=numpy.array(range(self.n_k))
|
|
|
|
for ik in mpi.slice_array(ikarray):
|
|
|
|
S = self.lattice_gf_matsubara(ik=ik,mu=mu,with_Sigma = with_Sigma, beta = beta)
|
|
S *= self.bz_weights[ik]
|
|
|
|
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
tmp = Gloc[icrsh].copy() # init temporary storage
|
|
for sig,gf in tmp: tmp[sig] <<= self.downfold(ik,icrsh,sig,S[sig],gf)
|
|
Gloc[icrsh] += tmp
|
|
|
|
#collect data from mpi:
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
Gloc[icrsh] <<= mpi.all_reduce(mpi.world,Gloc[icrsh],lambda x,y : x+y)
|
|
mpi.barrier()
|
|
|
|
|
|
# Gloc[:] is now the sum over k projected to the local orbitals.
|
|
# here comes the symmetrisation, if needed:
|
|
if (self.symm_op!=0): Gloc = self.Symm_corr.symmetrize(Gloc)
|
|
|
|
# Gloc is rotated to the local coordinate system:
|
|
if (self.use_rotations):
|
|
for icrsh in xrange(self.n_corr_shells):
|
|
for sig,gf in Gloc[icrsh]: Gloc[icrsh][sig] <<= self.rotloc(icrsh,gf,direction='toLocal')
|
|
|
|
# transform to CTQMC blocks:
|
|
Glocret = [ BlockGf( name_block_generator = [ (a,GfImFreq(indices = al, mesh = Gloc[0].mesh)) for a,al in self.gf_struct_solver[i] ],
|
|
make_copies = False) for i in xrange(self.n_inequiv_corr_shells) ]
|
|
for ish in xrange(self.n_inequiv_corr_shells):
|
|
|
|
# setting up the index map:
|
|
map_ind={}
|
|
cnt = {}
|
|
for blname in self.map[ish]:
|
|
cnt[blname] = 0
|
|
|
|
for a,al in self.gf_struct_solver[ish]:
|
|
blname = self.map_inv[ish][a]
|
|
map_ind[a] = range(len(al))
|
|
for i in al:
|
|
map_ind[a][i] = cnt[blname]
|
|
cnt[blname]+=1
|
|
|
|
|
|
for ibl in range(len(self.gf_struct_solver[ish])):
|
|
for i in range(len(self.gf_struct_solver[ish][ibl][1])):
|
|
for j in range(len(self.gf_struct_solver[ish][ibl][1])):
|
|
bl = self.gf_struct_solver[ish][ibl][0]
|
|
ind1 = self.gf_struct_solver[ish][ibl][1][i]
|
|
ind2 = self.gf_struct_solver[ish][ibl][1][j]
|
|
ind1_imp = map_ind[bl][ind1]
|
|
ind2_imp = map_ind[bl][ind2]
|
|
Glocret[ish][bl][ind1,ind2] <<= Gloc[self.invshellmap[ish]][self.map_inv[ish][bl]][ind1_imp,ind2_imp]
|
|
|
|
|
|
# return only the inequivalent shells:
|
|
return Glocret
|
|
|
|
|
|
def calc_density_correction(self,filename = 'dens_mat.dat'):
|
|
""" Calculates the density correction in order to feed it back to the DFT calculations."""
|
|
|
|
|
|
assert (type(filename)==StringType), "filename has to be a string!"
|
|
|
|
ntoi = self.names_to_ind[self.SO]
|
|
bln = self.block_names[self.SO]
|
|
|
|
# Set up deltaN:
|
|
deltaN = {}
|
|
for ib in bln:
|
|
deltaN[ib] = [ numpy.zeros( [self.n_orbitals[ik,ntoi[ib]],self.n_orbitals[ik,ntoi[ib]]], numpy.complex_) for ik in range(self.n_k)]
|
|
|
|
ikarray=numpy.array(range(self.n_k))
|
|
|
|
dens = {}
|
|
for ib in bln:
|
|
dens[ib] = 0.0
|
|
|
|
for ik in mpi.slice_array(ikarray):
|
|
|
|
S = self.lattice_gf_matsubara(ik=ik,mu=self.chemical_potential)
|
|
for sig,g in S:
|
|
deltaN[sig][ik] = S[sig].density()
|
|
dens[sig] += self.bz_weights[ik] * S[sig].total_density()
|
|
|
|
|
|
|
|
#put mpi Barrier:
|
|
for sig in deltaN:
|
|
for ik in range(self.n_k):
|
|
deltaN[sig][ik] = mpi.all_reduce(mpi.world,deltaN[sig][ik],lambda x,y : x+y)
|
|
dens[sig] = mpi.all_reduce(mpi.world,dens[sig],lambda x,y : x+y)
|
|
mpi.barrier()
|
|
|
|
|
|
# now save to file:
|
|
if (mpi.is_master_node()):
|
|
if (self.SP==0):
|
|
f=open(filename,'w')
|
|
else:
|
|
f=open(filename+'up','w')
|
|
f1=open(filename+'dn','w')
|
|
# write chemical potential (in Rydberg):
|
|
f.write("%.14f\n"%(self.chemical_potential/self.energy_unit))
|
|
if (self.SP!=0): f1.write("%.14f\n"%(self.chemical_potential/self.energy_unit))
|
|
# write beta in ryderg-1
|
|
f.write("%.14f\n"%(S.mesh.beta*self.energy_unit))
|
|
if (self.SP!=0): f1.write("%.14f\n"%(S.mesh.beta*self.energy_unit))
|
|
if (self.SP==0):
|
|
for ik in range(self.n_k):
|
|
f.write("%s\n"%self.n_orbitals[ik,0])
|
|
for inu in range(self.n_orbitals[ik,0]):
|
|
for imu in range(self.n_orbitals[ik,0]):
|
|
valre = (deltaN['up'][ik][inu,imu].real + deltaN['down'][ik][inu,imu].real) / 2.0
|
|
valim = (deltaN['up'][ik][inu,imu].imag + deltaN['down'][ik][inu,imu].imag) / 2.0
|
|
f.write("%.14f %.14f "%(valre,valim))
|
|
f.write("\n")
|
|
f.write("\n")
|
|
f.close()
|
|
elif ((self.SP==1)and(self.SO==0)):
|
|
for ik in range(self.n_k):
|
|
f.write("%s\n"%self.n_orbitals[ik,0])
|
|
for inu in range(self.n_orbitals[ik,0]):
|
|
for imu in range(self.n_orbitals[ik,0]):
|
|
f.write("%.14f %.14f "%(deltaN['up'][ik][inu,imu].real,deltaN['up'][ik][inu,imu].imag))
|
|
f.write("\n")
|
|
f.write("\n")
|
|
f.close()
|
|
for ik in range(self.n_k):
|
|
f1.write("%s\n"%self.n_orbitals[ik,1])
|
|
for inu in range(self.n_orbitals[ik,1]):
|
|
for imu in range(self.n_orbitals[ik,1]):
|
|
f1.write("%.14f %.14f "%(deltaN['down'][ik][inu,imu].real,deltaN['down'][ik][inu,imu].imag))
|
|
f1.write("\n")
|
|
f1.write("\n")
|
|
f1.close()
|
|
else:
|
|
for ik in range(self.n_k):
|
|
f.write("%s\n"%self.n_orbitals[ik,0])
|
|
for inu in range(self.n_orbitals[ik,0]):
|
|
for imu in range(self.n_orbitals[ik,0]):
|
|
f.write("%.14f %.14f "%(deltaN['ud'][ik][inu,imu].real,deltaN['ud'][ik][inu,imu].imag))
|
|
f.write("\n")
|
|
f.write("\n")
|
|
f.close()
|
|
for ik in range(self.n_k):
|
|
f1.write("%s\n"%self.n_orbitals[ik,0])
|
|
for inu in range(self.n_orbitals[ik,0]):
|
|
for imu in range(self.n_orbitals[ik,0]):
|
|
f1.write("%.14f %.14f "%(deltaN['ud'][ik][inu,imu].real,deltaN['ud'][ik][inu,imu].imag))
|
|
f1.write("\n")
|
|
f1.write("\n")
|
|
f1.close()
|
|
|
|
|
|
return deltaN, dens
|