################################################################################
#
# 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 .
#
################################################################################
from types import *
from symmetry import *
import numpy
import pytriqs.utility.dichotomy as dichotomy
from pytriqs.gf.local import *
from pytriqs.archive import *
import pytriqs.utility.mpi as mpi
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 = 'lda_input', symmcorr_data = 'lda_symmcorr_input',
parproj_data = 'lda_parproj_input', symmpar_data = 'lda_symmpar_input', bands_data = 'lda_bands_input'):
"""
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.symmcorr_data = symmcorr_data
self.parproj_data = parproj_data
self.symmpar_data = symmpar_data
self.bands_data = bands_data
self.block_names = [ ['up','down'], ['ud'] ]
self.n_spin_blocks_gf = [2,1]
self.G_upfold = 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']
self.read_value = self.read_input_from_hdf(subgrp=self.lda_data,things_to_read=things_to_read,optional_things=optional_things)
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!")
# determine the number of inequivalent correlated shells (self.n_inequiv_corr_shells)
# and related maps (self.shellmap, self.invshellmap)
self.inequiv_shells(self.corr_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
# Most general form allowing for all hybridisation, i.e. largest blocks possible
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.read_value['gf_struct_solver']):
# No gf_struct was stored in HDF, so first set a standard one:
self.gf_struct_solver = [ dict([ (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 range(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.read_value['dc_imp']):
# init the double counting:
self.__init_dc()
if not (self.read_value['chemical_potential']):
self.chemical_potential = mu
if not (self.read_value['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.symmcorr_data)
# Analyse the block structure and determine the smallest blocs, if desired
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
"""
read_value = True
# init variables on all nodes to ensure mpi broadcast works at the end
for it in things_to_read: setattr(self,it,0)
for it in optional_things: setattr(self,it,0)
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]):
setattr(self,it,ar[subgrp][it])
else:
mpi.report("Loading %s failed!"%it)
read_value = False
if ((read_value) and (len(optional_things)>0)):
# if necessary things worked, now read optional things:
read_value = {}
for it in optional_things:
if (it in ar[subgrp]):
setattr(self,it,ar[subgrp][it])
read_value['%s'%it] = True
else:
read_value['%s'%it] = False
else:
mpi.report("Loading failed: No %s subgroup in HDF5!"%subgrp)
read_value = False
del ar
# now do the broadcasting:
for it in things_to_read: setattr(self,it,mpi.bcast(getattr(self,it)))
for it in optional_things: setattr(self,it,mpi.bcast(getattr(self,it)))
read_value = mpi.bcast(read_value)
return read_value
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')
things_to_save=['chemical_potential','dc_imp','dc_energ']
for it in things_to_save: ar[self.lda_data][it] = getattr(self,it)
del ar
def load(self):
"""Loads some quantities from an HDF5 arxiv"""
things_to_read=['chemical_potential','dc_imp','dc_energ']
read_value = self.read_input_from_hdf(subgrp=self.lda_data,things_to_read=things_to_read)
return read_value
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) 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
# Do we need to set up G_upfold?
set_up_G_upfold = False # assume not
if self.G_upfold == None: # yes if not G_upfold provided
set_up_G_upfold = True
else: # yes if inconsistencies present in existing G_upfold
GFsize = [ gf.N1 for sig,gf in self.G_upfold]
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.G_upfold.mesh.beta != beta) ): set_up_G_upfold = True
# Set up G_upfold
if set_up_G_upfold:
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.G_upfold = BlockGf(name_list = a_list, block_list = glist(),make_copies=False)
self.G_upfold.zero()
self.G_upfold << iOmega_n
idmat = [numpy.identity(self.n_orbitals[ik,ntoi[bl]],numpy.complex_) for bl in bln]
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.G_upfold -= M
if (with_Sigma):
for icrsh in xrange(self.n_corr_shells):
for sig,gf in self.G_upfold: gf -= self.upfold(ik,icrsh,sig,stmp[icrsh][sig],gf)
self.G_upfold.invert()
return self.G_upfold
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): # ONLY WORKS FOR DIAGONAL HOPPING MATRIX (TRUE IN WIEN2K)
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
# calculate upfolded gf, then density matrix -- no assumptions on structure (ie diagonal or not)
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):
G_upfold = self.lattice_gf_matsubara(ik=ik, beta=beta, mu=self.chemical_potential)
G_upfold *= self.bz_weights[ik]
dm = G_upfold.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 Green function block structure from 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[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].update( [('%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]])=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
# for simply dft input, get crystal field splittings.
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.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_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 are using the correct interaction Hamiltonian!"""
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].iteritems():
bl = self.map_inv[iorb][a]
Ncr[bl] += dens_mat[a].real.trace()
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): # FLL
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): # Held's formula, with U_interact the interorbital onsite interaction
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)
for bl in a_list:
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)
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): # AMF
self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
for bl in a_list:
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 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 all(type(g) == GfImFreq for name,g in Sigma_imp[0]):
# 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) ]
elif all(type(g) == GfReFreq for name,g in Sigma_imp[0]):
# 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) ]
else:
raise ValueError, "This type of Sigma is not handled."
# 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].iteritems():
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 bl, orblist in self.gf_struct_solver[s].iteritems():
for i in range(len(orblist)):
for j in range(len(orblist)):
ind1 = orblist[i]
ind2 = orblist[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]:
# Transform dc_imp to global coordinate system
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 # list of self energies corrected by DC
def set_mu(self,mu):
"""Sets a new chemical potential"""
self.chemical_potential = mu
#print "Chemical potential in SumK set to ",mu
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 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 global 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].iteritems() ],
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].iteritems():
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 bl, orblist in self.gf_struct_solver[ish].iteritems():
for i in range(len(orblist)):
for j in range(len(orblist)):
ind1 = orblist[i]
ind2 = orblist[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
################
# FIXME LEAVE UNDOCUMENTED
################
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 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
# FIXME Check that dens matrix from projectors (DM=PPdagger) is correct (ie matches DFT)
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
# FIXME DETERMINE EQUIVALENCY OF SHELLS
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