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]
#print ik, bn, isp
dens_mat[icrsh][bn] += self.bz_weights[ik] * numpy.dot( numpy.dot(self.proj_mat[ik][isp][icrsh],MMat[ibn]) ,
self.proj_mat[ik][isp][icrsh].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 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
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)
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):
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]
Glocret[ish][bl][ind1,ind2] <<= Gloc[self.invshellmap[ish]][self.map_inv[ish][bl]][ind1,ind2]
# return only the inequivalent shells:
return Glocret
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]
#print ik, bn, isp
dens_mat[icrsh][bn] += numpy.dot( numpy.dot(self.proj_mat[ik][isp][icrsh],MMat[ibn]),self.proj_mat[ik][isp][icrsh].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 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 partial_charges(self):
"""Calculates the orbitally-resolved density matrix for all the orbitals considered in the input.
The theta-projectors are used, hence case.parproj data is necessary"""
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.par_proj_data,thingstoread=thingstoread)
retval = self.read_par_proj_input_from_hdf()
if not retval: return retval
if self.symm_op: self.Symm_par = Symmetry(self.hdf_file,subgroup=self.symm_par_data)
# Density matrix in the window
bln = self.blocnames[self.SO]
ntoi = self.names_to_ind[self.SO]
self.Dens_Mat_window = [ [numpy.zeros([self.shells[ish][3],self.shells[ish][3]],numpy.complex_) for ish in range(self.N_shells)]
for isp in range(len(bln)) ] # init the density matrix
mu = self.Chemical_Potential
GFStruct_proj = [ [ (al, range(self.shells[i][3])) for al in bln ] for i in xrange(self.N_shells) ]
if hasattr(self,"Sigma_imp"):
Gproj = [BlockGf(name_block_generator = [ (a,GfImFreq(indices = al, mesh = self.Sigma_imp[0].mesh)) for a,al in GFStruct_proj[ish] ], make_copies = False)
for ish in xrange(self.N_shells)]
else:
Gproj = [BlockGf(name_block_generator = [ (a,GfImFreq(indices = al, beta = 40)) for a,al in GFStruct_proj[ish] ], make_copies = False)
for ish in xrange(self.N_shells)]
for ish in xrange(self.N_shells): Gproj[ish].zero()
ikarray=numpy.array(range(self.Nk))
#print mpi.rank, mpi.slice_array(ikarray)
#print "K-Sum starts on node",mpi.rank," at ",datetime.now()
for ik in mpi.slice_array(ikarray):
#print mpi.rank, ik, datetime.now()
S = self.latticeGF_Matsubara(ik=ik,mu=mu)
S *= self.BZ_weights[ik]
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig,gf in tmp: tmp[sig] <<= self.downfold_pc(ik,ir,ish,sig,S[sig],gf)
Gproj[ish] += tmp
#print "K-Sum done on node",mpi.rank," at ",datetime.now()
#collect data from mpi:
for ish in xrange(self.N_shells):
Gproj[ish] <<= mpi.all_reduce(mpi.world,Gproj[ish],lambda x,y : x+y)
mpi.barrier()
#print "Data collected on node",mpi.rank," at ",datetime.now()
# Symmetrisation:
if (self.symm_op!=0): Gproj = self.Symm_par.symmetrize(Gproj)
#print "Symmetrisation done on node",mpi.rank," at ",datetime.now()
for ish in xrange(self.N_shells):
# Rotation to local:
if (self.use_rotations):
for sig,gf in Gproj[ish]: Gproj[ish][sig] <<= self.rotloc_all(ish,gf,direction='toLocal')
isp = 0
for sig,gf in Gproj[ish]: #dmg.append(Gproj[ish].density()[sig])
self.Dens_Mat_window[isp][ish] = Gproj[ish].density()[sig]
isp+=1
# add Density matrices to get the total:
Dens_Mat = [ [ self.Dens_Mat_below[ntoi[bln[isp]]][ish]+self.Dens_Mat_window[isp][ish] for ish in range(self.N_shells)]
for isp in range(len(bln)) ]
return Dens_Mat
def dos_partial(self,broadening=0.01):
"""calculates the orbitally-resolved DOS"""
assert hasattr(self,"Sigma_imp"), "Set Sigma First!!"
#thingstoread = ['Dens_Mat_below','N_parproj','Proj_Mat_pc','rotmat_all']
#retval = self.read_input_from_HDF(SubGrp=self.par_proj_data, thingstoread=thingstoread)
retval = self.read_par_proj_input_from_hdf()
if not retval: return retval
if self.symm_op: self.Symm_par = Symmetry(self.hdf_file,subgroup=self.symm_par_data)
mu = self.Chemical_Potential
GFStruct_proj = [ [ (al, range(self.shells[i][3])) for al in self.blocnames[self.SO] ] for i in xrange(self.N_shells) ]
Gproj = [BlockGf(name_block_generator = [ (a,GfReFreq(indices = al, mesh = self.Sigma_imp[0].mesh)) for a,al in GFStruct_proj[ish] ], make_copies = False )
for ish in xrange(self.N_shells)]
for ish in range(self.N_shells): Gproj[ish].zero()
Msh = [x for x in self.Sigma_imp[0].mesh]
n_om = len(Msh)
DOS = {}
for bn in self.blocnames[self.SO]:
DOS[bn] = numpy.zeros([n_om],numpy.float_)
DOSproj = [ {} for ish in range(self.N_shells) ]
DOSproj_orb = [ {} for ish in range(self.N_shells) ]
for ish in range(self.N_shells):
for bn in self.blocnames[self.SO]:
dl = self.shells[ish][3]
DOSproj[ish][bn] = numpy.zeros([n_om],numpy.float_)
DOSproj_orb[ish][bn] = numpy.zeros([dl,dl,n_om],numpy.float_)
ikarray=numpy.array(range(self.Nk))
for ik in mpi.slice_array(ikarray):
S = self.lattice_gf_realfreq(ik=ik,mu=mu,broadening=broadening)
S *= self.BZ_weights[ik]
# non-projected DOS
for iom in range(n_om):
for sig,gf in S: DOS[sig][iom] += gf._data.array[:,:,iom].imag.trace()/(-3.1415926535)
#projected DOS:
for ish in xrange(self.N_shells):
tmp = Gproj[ish].copy()
for ir in xrange(self.N_parproj[ish]):
for sig,gf in tmp: tmp[sig] <<= self.downfold_pc(ik,ir,ish,sig,S[sig],gf)
Gproj[ish] += tmp
# collect data from mpi:
for sig in DOS:
DOS[sig] = mpi.all_reduce(mpi.world,DOS[sig],lambda x,y : x+y)
for ish in xrange(self.N_shells):
Gproj[ish] <<= mpi.all_reduce(mpi.world,Gproj[ish],lambda x,y : x+y)
mpi.barrier()
if (self.symm_op!=0): Gproj = self.Symm_par.symmetrize(Gproj)
# rotation to local coord. system:
if (self.use_rotations):
for ish in xrange(self.N_shells):
for sig,gf in Gproj[ish]: Gproj[ish][sig] <<= self.rotloc_all(ish,gf,direction='toLocal')
for ish in range(self.N_shells):
for sig,gf in Gproj[ish]:
for iom in range(n_om): DOSproj[ish][sig][iom] += gf._data.array[:,:,iom].imag.trace()/(-3.1415926535)
DOSproj_orb[ish][sig][:,:,:] += gf._data.array[:,:,:].imag / (-3.1415926535)
if (mpi.is_master_node()):
# output to files
for bn in self.blocnames[self.SO]:
f=open('./DOScorr%s.dat'%bn, 'w')
for i in range(n_om): f.write("%s %s\n"%(Msh[i],DOS[bn][i]))
f.close()
# partial
for ish in range(self.N_shells):
f=open('DOScorr%s_proj%s.dat'%(bn,ish),'w')
for i in range(n_om): f.write("%s %s\n"%(Msh[i],DOSproj[ish][bn][i]))
f.close()
for i in range(self.shells[ish][3]):
for j in range(i,self.shells[ish][3]):
Fname = './DOScorr'+bn+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat'
f=open(Fname,'w')
for iom in range(n_om): f.write("%s %s\n"%(Msh[iom],DOSproj_orb[ish][bn][i,j,iom]))
f.close()
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.beta*self.energy_unit))
if (self.SP!=0): f1.write("%.14f\n"%(S.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