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54caa08069
dft_tools/python/sumk_dft_tools.py
Manuel Zingl 54caa08069 Fixes two bugs in dos_*_basis 
1.) Missing minus
2.) wrong summation index i -> iom
2015-03-30 17:49:46 +02:00

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################################################################################
#
# 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 *
import numpy
from pytriqs.gf.local import *
import pytriqs.utility.mpi as mpi
from symmetry import *
from sumk_dft import SumkDFT
class SumkDFTTools(SumkDFT):
"""Extends the SumkDFT class with some tools for analysing the data."""
def __init__(self, hdf_file, h_field = 0.0, use_dft_blocks = False, dft_data = 'dft_input', symmcorr_data = 'dft_symmcorr_input',
parproj_data = 'dft_parproj_input', symmpar_data = 'dft_symmpar_input', bands_data = 'dft_bands_input',
transp_data = 'dft_transp_input', misc_data = 'dft_misc_input'):
SumkDFT.__init__(self, hdf_file=hdf_file, h_field=h_field, use_dft_blocks=use_dft_blocks,
dft_data=dft_data, symmcorr_data=symmcorr_data, parproj_data=parproj_data,
symmpar_data=symmpar_data, bands_data=bands_data, transp_data=transp_data,
misc_data=misc_data)
def dos_wannier_basis(self, mu=None, broadening=None, mesh=None, with_Sigma=True, with_dc=True, save_to_file=True):
if (mesh is None) and (not with_Sigma):
raise ValueError, "lattice_gf: Give the mesh=(om_min,om_max,n_points) for the lattice GfReFreq."
if mesh is None:
om_mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
om_min = om_mesh[0]
om_max = om_mesh[-1]
n_om = len(om_mesh)
mesh = (om_min,om_max,n_om)
else:
om_min,om_max,n_om = mesh
delta_om = (om_max-om_min)/(n_om-1)
om_mesh = [om_min + delta_om * i for i in range(n_om)]
G_loc = []
for icrsh in range(self.n_corr_shells):
spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
glist = [ GfReFreq(indices = inner, window = (om_min,om_max), n_points = n_om) for block,inner in self.gf_struct_sumk[icrsh]]
G_loc.append(BlockGf(name_list = spn, block_list = glist, make_copies=False))
for icrsh in range(self.n_corr_shells): G_loc[icrsh].zero()
DOS = { sp: numpy.zeros([n_om],numpy.float_) for sp in self.spin_block_names[self.SO] }
DOSproj = [ {} for ish in range(self.n_inequiv_shells) ]
DOSproj_orb = [ {} for ish in range(self.n_inequiv_shells) ]
for ish in range(self.n_inequiv_shells):
for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]]['SO']]:
dim = self.corr_shells[self.inequiv_to_corr[ish]]['dim']
DOSproj[ish][sp] = numpy.zeros([n_om],numpy.float_)
DOSproj_orb[ish][sp] = numpy.zeros([n_om,dim,dim],numpy.float_)
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening,mesh=mesh,with_Sigma=with_Sigma,with_dc=with_dc)
G_latt_w *= self.bz_weights[ik]
# Non-projected DOS
for iom in range(n_om):
for bname,gf in G_latt_w:
DOS[bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
# Projected DOS:
for icrsh in range(self.n_corr_shells):
tmp = G_loc[icrsh].copy()
for bname,gf in tmp: tmp[bname] << self.downfold(ik,icrsh,bname,G_latt_w[bname],gf) # downfolding G
G_loc[icrsh] += tmp
# Collect data from mpi:
for bname in DOS:
DOS[bname] = mpi.all_reduce(mpi.world, DOS[bname], lambda x,y : x+y)
for ish in range(self.n_shells):
G_loc[ish] << mpi.all_reduce(mpi.world, G_loc[ish], lambda x,y : x+y)
mpi.barrier()
# Symmetrize and rotate to local coord. system if needed:
if self.symm_op != 0: G_loc = self.symmcorr.symmetrize(G_loc)
if self.use_rotations:
for icrsh in range(self.n_corr_shells):
for bname,gf in G_loc[icrsh]: G_loc[icrsh][bname] << self.rotloc(icrsh,gf,direction='toLocal')
# G_loc can now also be used to look at orbitally-resolved quantities
for ish in range(self.n_inequiv_shells):
for bname,gf in G_loc[self.inequiv_to_corr[ish]]: # loop over spins
for iom in range(n_om): DOSproj[ish][bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
DOSproj_orb[ish][bname][:,:,:] -= gf.data[:,:,:].imag/numpy.pi
# Write to files
if save_to_file and mpi.is_master_node():
for sp in self.spin_block_names[self.SO]:
f = open('DOS_wann_%s.dat'%sp, 'w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOS[sp][iom]))
f.close()
# Partial
for ish in range(self.n_inequiv_shells):
f = open('DOS_wann_%s_proj%s.dat'%(sp,ish),'w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOSproj[ish][sp][iom]))
f.close()
# Orbitally-resolved
for i in range(self.corr_shells[self.inequiv_to_corr[ish]]['dim']):
for j in range(i,self.corr_shells[self.inequiv_to_corr[ish]]['dim']):
f = open('DOS_wann_'+sp+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat','w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOSproj_orb[ish][sp][iom,i,j]))
f.close()
return DOS, DOSproj, DOSproj_orb
def dos_parproj_basis(self, mu=None, broadening=None, mesh=None, with_Sigma=True, with_dc=True, save_to_file=True):
"""Calculates the orbitally-resolved DOS"""
things_to_read = ['n_parproj','proj_mat_all','rot_mat_all','rot_mat_all_time_inv']
value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
if not value_read: return value_read
if self.symm_op: self.symmpar = Symmetry(self.hdf_file,subgroup=self.symmpar_data)
if (mesh is None) and (not with_Sigma):
raise ValueError, "lattice_gf: Give the mesh=(om_min,om_max,n_points) for the lattice GfReFreq."
if mesh is None:
om_mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
om_min = om_mesh[0]
om_max = om_mesh[-1]
n_om = len(om_mesh)
mesh = (om_min,om_max,n_om)
else:
om_min,om_max,n_om = mesh
delta_om = (om_max-om_min)/(n_om-1)
om_mesh = [om_min + delta_om * i for i in range(n_om)]
G_loc = []
spn = self.spin_block_names[self.SO]
gf_struct_parproj = [ [ (sp, range(self.shells[ish]['dim'])) for sp in spn ]
for ish in range(self.n_shells) ]
for ish in range(self.n_shells):
glist = [ GfReFreq(indices = inner, window = (om_min,om_max), n_points = n_om) for block,inner in gf_struct_parproj[ish] ]
G_loc.append(BlockGf(name_list = spn, block_list = glist, make_copies=False))
for ish in range(self.n_shells): G_loc[ish].zero()
DOS = { sp: numpy.zeros([n_om],numpy.float_) for sp in self.spin_block_names[self.SO] }
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 sp in self.spin_block_names[self.SO]:
dim = self.shells[ish]['dim']
DOSproj[ish][sp] = numpy.zeros([n_om],numpy.float_)
DOSproj_orb[ish][sp] = numpy.zeros([n_om,dim,dim],numpy.float_)
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening,mesh=mesh,with_Sigma=with_Sigma,with_dc=with_dc)
G_latt_w *= self.bz_weights[ik]
# Non-projected DOS
for iom in range(n_om):
for bname,gf in G_latt_w:
DOS[bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
# Projected DOS:
for ish in range(self.n_shells):
tmp = G_loc[ish].copy()
for ir in range(self.n_parproj[ish]):
for bname,gf in tmp: tmp[bname] << self.downfold(ik,ish,bname,G_latt_w[bname],gf,shells='all',ir=ir)
G_loc[ish] += tmp
# Collect data from mpi:
for bname in DOS:
DOS[bname] = mpi.all_reduce(mpi.world, DOS[bname], lambda x,y : x+y)
for ish in range(self.n_shells):
G_loc[ish] << mpi.all_reduce(mpi.world, G_loc[ish], lambda x,y : x+y)
mpi.barrier()
# Symmetrize and rotate to local coord. system if needed:
if self.symm_op != 0: G_loc = self.symmpar.symmetrize(G_loc)
if self.use_rotations:
for ish in range(self.n_shells):
for bname,gf in G_loc[ish]: G_loc[ish][bname] << self.rotloc(ish,gf,direction='toLocal',shells='all')
# G_loc can now also be used to look at orbitally-resolved quantities
for ish in range(self.n_shells):
for bname,gf in G_loc[ish]:
for iom in range(n_om): DOSproj[ish][bname][iom] -= gf.data[iom,:,:].imag.trace()/numpy.pi
DOSproj_orb[ish][bname][:,:,:] -= gf.data[:,:,:].imag/numpy.pi
# Write to files
if save_to_file and mpi.is_master_node():
for sp in self.spin_block_names[self.SO]:
f = open('DOS_parproj_%s.dat'%sp, 'w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOS[sp][iom]))
f.close()
# Partial
for ish in range(self.n_shells):
f = open('DOS_parproj_%s_proj%s.dat'%(sp,ish),'w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOSproj[ish][sp][iom]))
f.close()
# Orbitally-resolved
for i in range(self.shells[ish]['dim']):
for j in range(i,self.shells[ish]['dim']):
f = open('DOS_parproj_'+sp+'_proj'+str(ish)+'_'+str(i)+'_'+str(j)+'.dat','w')
for iom in range(n_om): f.write("%s %s\n"%(om_mesh[iom],DOSproj_orb[ish][sp][iom,i,j]))
f.close()
return DOS, DOSproj, DOSproj_orb
def spaghettis(self,broadening,plot_shift=0.0,plot_range=None,ishell=None,invert_Akw=False,fermi_surface=False,mu=None,save_to_file=True):
""" Calculates the correlated band structure with a real-frequency self energy."""
assert hasattr(self,"Sigma_imp_w"), "spaghettis: Set Sigma_imp_w first."
things_to_read = ['n_k','n_orbitals','proj_mat','hopping','n_parproj','proj_mat_all']
value_read = self.read_input_from_hdf(subgrp=self.bands_data,things_to_read=things_to_read)
if not value_read: return value_read
things_to_read = ['rot_mat_all','rot_mat_all_time_inv']
value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
if not value_read: return value_read
if mu is None: mu = self.chemical_potential
spn = self.spin_block_names[self.SO]
mesh = [x.real for x in self.Sigma_imp_w[0].mesh]
n_om = len(mesh)
if plot_range is None:
om_minplot = mesh[0] - 0.001
om_maxplot = mesh[n_om-1] + 0.001
else:
om_minplot = plot_range[0]
om_maxplot = plot_range[1]
if ishell is None:
Akw = { sp: numpy.zeros([self.n_k,n_om],numpy.float_) for sp in spn }
else:
Akw = { sp: numpy.zeros([self.shells[ishell]['dim'],self.n_k,n_om],numpy.float_) for sp in spn }
if fermi_surface:
ishell = None
Akw = { sp: numpy.zeros([self.n_k,1],numpy.float_) for sp in spn }
om_minplot = -2.0*broadening
om_maxplot = 2.0*broadening
if not ishell is None:
gf_struct_parproj = [ (sp, range(self.shells[ishell]['dim'])) for sp in spn ]
G_loc = BlockGf(name_block_generator = [ (block,GfReFreq(indices = inner, mesh = self.Sigma_imp_w[0].mesh))
for block,inner in gf_struct_parproj ], make_copies = False)
G_loc.zero()
for ik in range(self.n_k):
G_latt_w = self.lattice_gf(ik=ik,mu=mu,iw_or_w="w",broadening=broadening)
if ishell is None:
# Non-projected A(k,w)
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
if fermi_surface:
for bname,gf in G_latt_w: Akw[bname][ik,0] += gf.data[iom,:,:].imag.trace()/(-1.0*numpy.pi) * (mesh[1]-mesh[0])
else:
for bname,gf in G_latt_w: Akw[bname][ik,iom] += gf.data[iom,:,:].imag.trace()/(-1.0*numpy.pi)
Akw[bname][ik,iom] += ik*plot_shift # shift Akw for plotting stacked k-resolved eps(k) curves
if invert_Akw:
for sp in spn: # loop over GF blocs:
maxAkw = Akw[sp].max()
minAkw = Akw[sp].min()
if fermi_surface:
Akw[sp][ik,0] = 1.0/(minAkw-maxAkw)*(Akw[sp][ik,0] - maxAkw)
else:
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
Akw[sp][ik,iom] = 1.0/(minAkw-maxAkw)*(Akw[sp][ik,iom] - maxAkw)
else: # ishell not None
# Projected A(k,w):
G_loc.zero()
tmp = G_loc.copy()
for ir in range(self.n_parproj[ishell]):
for bname,gf in tmp: tmp[bname] << self.downfold(ik,ishell,bname,G_latt_w[bname],gf,shells='all',ir=ir)
G_loc += tmp
# Rotate to local frame
if self.use_rotations:
for bname,gf in G_loc: G_loc[bname] << self.rotloc(ishell,gf,direction='toLocal',shells='all')
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
for ish in range(self.shells[ishell]['dim']):
for sp in spn:
Akw[sp][ish,ik,iom] = G_loc[sp].data[iom,ish,ish].imag/(-1.0*numpy.pi)
if invert_Akw:
for sp in spn:
for ish in range(self.shells[ishell]['dim']):
maxAkw=Akw[sp][ish,:,:].max()
minAkw=Akw[sp][ish,:,:].min()
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
Akw[sp][ish,ik,iom] = 1.0/(minAkw-maxAkw)*(Akw[sp][ish,ik,iom] - maxAkw)
if save_to_file and mpi.is_master_node():
if ishell is None:
for sp in spn: # loop over GF blocs:
# Open file for storage:
if fermi_surface:
f = open('FS_'+sp+'.dat','w')
else:
f = open('Akw_'+sp+'.dat','w')
for ik in range(self.n_k):
if fermi_surface:
f.write('%s %s\n'%(ik,Akw[sp][ik,0]))
else:
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
if plot_shift > 0.0001:
f.write('%s %s\n'%(mesh[iom],Akw[sp][ik,iom]))
else:
f.write('%s %s %s\n'%(ik,mesh[iom],Akw[sp][ik,iom]))
f.write('\n')
f.close()
else: # ishell is not None
for sp in spn:
for ish in range(self.shells[ishell]['dim']):
f = open('Akw_'+sp+'_proj'+str(ish)+'.dat','w')
for ik in range(self.n_k):
for iom in range(n_om):
if (mesh[iom] > om_minplot) and (mesh[iom] < om_maxplot):
if plot_shift > 0.0001:
f.write('%s %s\n'%(mesh[iom],Akw[sp][ish,ik,iom]))
else:
f.write('%s %s %s\n'%(ik,mesh[iom],Akw[sp][ish,ik,iom]))
f.write('\n')
f.close()
return Akw
def partial_charges(self,beta=40,mu=None,with_Sigma=True,with_dc=True):
"""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"""
things_to_read = ['dens_mat_below','n_parproj','proj_mat_all','rot_mat_all','rot_mat_all_time_inv']
value_read = self.read_input_from_hdf(subgrp=self.parproj_data,things_to_read = things_to_read)
if not value_read: return value_read
if self.symm_op: self.symmpar = Symmetry(self.hdf_file,subgroup=self.symmpar_data)
spn = self.spin_block_names[self.SO]
ntoi = self.spin_names_to_ind[self.SO]
# Density matrix in the window
self.dens_mat_window = [ [ numpy.zeros([self.shells[ish]['dim'],self.shells[ish]['dim']],numpy.complex_)
for ish in range(self.n_shells) ]
for isp in range(len(spn)) ]
# Set up G_loc
gf_struct_parproj = [ [ (sp, range(self.shells[ish]['dim'])) for sp in spn ]
for ish in range(self.n_shells) ]
if with_Sigma:
G_loc = [ BlockGf(name_block_generator = [ (block,GfImFreq(indices = inner, mesh = self.Sigma_imp_iw[0].mesh))
for block,inner in gf_struct_parproj[ish] ], make_copies = False)
for ish in range(self.n_shells)]
beta = self.Sigma_imp_iw[0].mesh.beta
else:
G_loc = [ BlockGf(name_block_generator = [ (block,GfImFreq(indices = inner, beta = beta))
for block,inner in gf_struct_parproj[ish] ], make_copies = False)
for ish in range(self.n_shells)]
for ish in range(self.n_shells): G_loc[ish].zero()
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
G_latt_iw = self.lattice_gf(ik=ik,mu=mu,iw_or_w="iw",beta=beta,with_Sigma=with_Sigma,with_dc=with_dc)
G_latt_iw *= self.bz_weights[ik]
for ish in range(self.n_shells):
tmp = G_loc[ish].copy()
for ir in range(self.n_parproj[ish]):
for bname,gf in tmp: tmp[bname] << self.downfold(ik,ish,bname,G_latt_iw[bname],gf,shells='all',ir=ir)
G_loc[ish] += tmp
# Collect data from mpi:
for ish in range(self.n_shells):
G_loc[ish] << mpi.all_reduce(mpi.world, G_loc[ish], lambda x,y : x+y)
mpi.barrier()
# Symmetrize and rotate to local coord. system if needed:
if self.symm_op != 0: G_loc = self.symmpar.symmetrize(G_loc)
if self.use_rotations:
for ish in range(self.n_shells):
for bname,gf in G_loc[ish]: G_loc[ish][bname] << self.rotloc(ish,gf,direction='toLocal',shells='all')
for ish in range(self.n_shells):
isp = 0
for bname,gf in G_loc[ish]:
self.dens_mat_window[isp][ish] = G_loc[ish].density()[bname]
isp += 1
# Add density matrices to get the total:
dens_mat = [ [ self.dens_mat_below[ntoi[spn[isp]]][ish] + self.dens_mat_window[isp][ish]
for ish in range(self.n_shells) ]
for isp in range(len(spn)) ]
return dens_mat
def print_hamiltonian(self):
""" Print Hamiltonian for checks."""
if self.SP == 1 and self.SO == 0:
f1 = open('hamup.dat','w')
f2 = open('hamdn.dat','w')
for ik in range(self.n_k):
for i in range(self.n_orbitals[ik,0]):
f1.write('%s %s\n'%(ik,self.hopping[ik,0,i,i].real))
for i in range(self.n_orbitals[ik,1]):
f2.write('%s %s\n'%(ik,self.hopping[ik,1,i,i].real))
f1.write('\n')
f2.write('\n')
f1.close()
f2.close()
else:
f = open('ham.dat','w')
for ik in range(self.n_k):
for i in range(self.n_orbitals[ik,0]):
f.write('%s %s\n'%(ik,self.hopping[ik,0,i,i].real))
f.write('\n')
f.close()
# ----------------- transport -----------------------
def read_transport_input_from_hdf(self):
"""
Reads the data for transport calculations from the HDF file
"""
thingstoread = ['band_window_optics','velocities_k']
self.read_input_from_hdf(subgrp=self.transp_data,things_to_read = thingstoread)
thingstoread = ['band_window','lattice_angles','lattice_constants','lattice_type','n_symmetries','rot_symmetries']
self.read_input_from_hdf(subgrp=self.misc_data,things_to_read = thingstoread)
def cellvolume(self, lattice_type, lattice_constants, latticeangle):
"""
Calculate cell volume: volumecc conventional cell, volumepc, primitive cell.
"""
a = lattice_constants[0]
b = lattice_constants[1]
c = lattice_constants[2]
c_al = numpy.cos(latticeangle[0])
c_be = numpy.cos(latticeangle[1])
c_ga = numpy.cos(latticeangle[2])
volumecc = a * b * c * numpy.sqrt(1 + 2 * c_al * c_be * c_ga - c_al ** 2 - c_be * 82 - c_ga ** 2)
det = {"P":1, "F":4, "B":2, "R":3, "H":1, "CXY":2, "CYZ":2, "CXZ":2}
volumepc = volumecc / det[lattice_type]
return volumecc, volumepc
def transport_distribution(self, directions=['xx'], energy_window=None, Om_mesh=[0.0], beta=40.0, with_Sigma=False, n_om=None, broadening=0.0):
"""
calculate Tr A(k,w) v(k) A(k, w+Om) v(k).
energy_window: regime for omega integral
Om_mesh: mesh for optic conductivitity. Om_mesh is repinned to the self-energy mesh!
directions: list of directions: xx,yy,zz,xy,yz,zx.
with_Sigma: Use Sigma_w = 0 if False (In this case it is necessary to specifiy the energywindow (energy_window),
the number of omega points (n_om) in the window and the broadening (broadening)).
"""
# Check if wien converter was called and read transport subgroup form hdf file
if mpi.is_master_node():
ar = HDFArchive(self.hdf_file, 'a')
if not (self.transp_data in ar): raise IOError, "transport_distribution: No %s subgroup in hdf file found! Call convert_transp_input first." %self.transp_data
self.read_transport_input_from_hdf()
if mpi.is_master_node():
# k-dependent-projections.
assert self.k_dep_projection == 1, "transport_distribution: k dependent projection is not implemented!"
# positive Om_mesh
assert all(Om >= 0.0 for Om in Om_mesh), "transport_distribution: Om_mesh should not contain negative values!"
# Check if energy_window is sufficiently large and correct
if (energy_window[0] >= energy_window[1] or energy_window[0] >= 0 or energy_window[1] <= 0):
assert 0, "transport_distribution: energy_window wrong!"
if (abs(self.fermi_dis(energy_window[0]*beta)*self.fermi_dis(-energy_window[0]*beta)) > 1e-5
or abs(self.fermi_dis(energy_window[1]*beta)*self.fermi_dis(-energy_window[1]*beta)) > 1e-5):
mpi.report("\n####################################################################")
mpi.report("transport_distribution: WARNING - energy window might be too narrow!")
mpi.report("####################################################################\n")
n_inequiv_spin_blocks = self.SP + 1 - self.SO # up and down are equivalent if SP = 0
self.directions = directions
dir_to_int = {'x':0, 'y':1, 'z':2}
# calculate A(k,w)
#######################################
# Define mesh for Greens function and in the specified energy window
if (with_Sigma == True):
self.omega = numpy.array([round(x.real,12) for x in self.Sigma_imp_w[0].mesh])
mesh = None
mu = self.chemical_potential
n_om = len(self.omega)
mpi.report("Using omega mesh provided by Sigma!")
if energy_window is not None:
# Find according window in Sigma mesh
ioffset = numpy.sum(self.omega < energy_window[0]-max(Om_mesh))
self.omega = self.omega[numpy.logical_and(self.omega >= energy_window[0]-max(Om_mesh), self.omega <= energy_window[1]+max(Om_mesh))]
n_om = len(self.omega)
# Truncate Sigma to given omega window
# In the future there should be an option in gf to manipulate the mesh (e.g. truncate) directly.
# For now we stick with this:
for icrsh in range(self.n_corr_shells):
Sigma_save = self.Sigma_imp_w[icrsh].copy()
spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
glist = lambda : [ GfReFreq(indices = inner, window=(self.omega[0], self.omega[-1]),n_points=n_om) for block, inner in self.gf_struct_sumk[icrsh]]
self.Sigma_imp_w[icrsh] = BlockGf(name_list = spn, block_list = glist(),make_copies=False)
for i,g in self.Sigma_imp_w[icrsh]:
for iL in g.indices:
for iR in g.indices:
for iom in xrange(n_om):
g.data[iom,iL,iR] = Sigma_save[i].data[ioffset+iom,iL,iR]
else:
assert n_om is not None, "transport_distribution: Number of omega points (n_om) needed to calculate transport distribution!"
assert energy_window is not None, "transport_distribution: Energy window needed to calculate transport distribution!"
assert broadening != 0.0 and broadening is not None, "transport_distribution: Broadening necessary to calculate transport distribution!"
self.omega = numpy.linspace(energy_window[0]-max(Om_mesh),energy_window[1]+max(Om_mesh),n_om)
mesh = [energy_window[0]-max(Om_mesh), energy_window[1]+max(Om_mesh), n_om]
mu = 0.0
# Define mesh for optic conductivity
d_omega = round(numpy.abs(self.omega[0] - self.omega[1]), 12)
iOm_mesh = numpy.array([round((Om / d_omega),0) for Om in Om_mesh])
self.Om_mesh = iOm_mesh * d_omega
if mpi.is_master_node():
print "Chemical potential: ", mu
print "Using n_om = %s points in the energy_window [%s,%s]"%(n_om, self.omega[0], self.omega[-1]),
print "where the omega vector is:"
print self.omega
print "Calculation requested for Omega mesh: ", numpy.array(Om_mesh)
print "Omega mesh automatically repinned to: ", self.Om_mesh
self.Gamma_w = {direction: numpy.zeros((len(self.Om_mesh), n_om), dtype=numpy.float_) for direction in self.directions}
# Sum over all k-points
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
# Calculate G_w for ik and initialize A_kw
G_w = self.lattice_gf(ik, mu, iw_or_w="w", beta=beta, broadening=broadening, mesh=mesh, with_Sigma=with_Sigma)
A_kw = [numpy.zeros((self.n_orbitals[ik][isp], self.n_orbitals[ik][isp], n_om), dtype=numpy.complex_)
for isp in range(n_inequiv_spin_blocks)]
for isp in range(n_inequiv_spin_blocks):
# Obtain A_kw from G_w (swapaxes is used to have omega in the 3rd dimension)
A_kw[isp].real = -copy.deepcopy(G_w[self.spin_block_names[self.SO][isp]].data.swapaxes(0,1).swapaxes(1,2)).imag / numpy.pi
b_min = max(self.band_window[isp][ik, 0], self.band_window_optics[isp][ik, 0])
b_max = min(self.band_window[isp][ik, 1], self.band_window_optics[isp][ik, 1])
A_i = slice(b_min - self.band_window[isp][ik, 0], b_max - self.band_window[isp][ik, 0] + 1)
v_i = slice(b_min - self.band_window_optics[isp][ik, 0], b_max - self.band_window_optics[isp][ik, 0] + 1)
# loop over all symmetries
for R in self.rot_symmetries:
# get transformed velocity under symmetry R
vel_R = copy.deepcopy(self.velocities_k[isp][ik])
for nu1 in range(self.band_window_optics[isp][ik, 1] - self.band_window_optics[isp][ik, 0] + 1):
for nu2 in range(self.band_window_optics[isp][ik, 1] - self.band_window_optics[isp][ik, 0] + 1):
vel_R[nu1][nu2][:] = numpy.dot(R, vel_R[nu1][nu2][:])
# calculate Gamma_w for each direction from the velocities vel_R and the spectral function A_kw
for direction in self.directions:
for iw in xrange(n_om):
for iq in range(len(self.Om_mesh)):
if(iw + iOm_mesh[iq] >= n_om or self.omega[iw] < -self.Om_mesh[iq] + energy_window[0] or self.omega[iw] > self.Om_mesh[iq] + energy_window[1]): continue
self.Gamma_w[direction][iq, iw] += (numpy.dot(numpy.dot(numpy.dot(vel_R[v_i, v_i, dir_to_int[direction[0]]],
A_kw[isp][A_i, A_i, iw]), vel_R[v_i, v_i, dir_to_int[direction[1]]]),
A_kw[isp][A_i, A_i, iw + iOm_mesh[iq]]).trace().real * self.bz_weights[ik])
for direction in self.directions:
self.Gamma_w[direction] = (mpi.all_reduce(mpi.world, self.Gamma_w[direction], lambda x, y : x + y)
/ self.cellvolume(self.lattice_type, self.lattice_constants, self.lattice_angles)[1] / self.n_symmetries)
def transport_coefficient(self, direction, iq=0, n=0, beta=40):
"""
calculates the transport coefficients A_n in a given direction and for a given Omega. (see documentation)
A_1 is set to nan if requested for Omega != 0.0
iq: index of Omega point in Om_mesh
direction: 'xx','yy','zz','xy','xz','yz'
"""
if not (mpi.is_master_node()): return
assert hasattr(self,'Gamma_w'), "transport_coefficient: Run transport_distribution first or load data from h5!"
A = 0.0
omegaT = self.omega * beta
d_omega = self.omega[1] - self.omega[0]
if (self.Om_mesh[iq] == 0.0):
for iw in xrange(self.Gamma_w[direction].shape[1]):
A += self.Gamma_w[direction][iq, iw] * self.fermi_dis(omegaT[iw]) * self.fermi_dis(-omegaT[iw]) * numpy.float(omegaT[iw])**n * d_omega
elif (n == 0.0):
for iw in xrange(self.Gamma_w[direction].shape[1]):
A += (self.Gamma_w[direction][iq, iw] * (self.fermi_dis(omegaT[iw]) - self.fermi_dis(omegaT[iw] + self.Om_mesh[iq] * beta))
/ (self.Om_mesh[iq] * beta) * d_omega)
else:
A = numpy.nan
return A * numpy.pi * (2.0-self.SP)
def conductivity_and_seebeck(self, beta=40):
"""
Calculates the Seebeck coefficient and the conductivity for a given Gamma_w
"""
if not (mpi.is_master_node()): return
assert hasattr(self,'Gamma_w'), "conductivity_and_seebeck: Run transport_distribution first or load data from h5!"
n_q = self.Gamma_w[self.directions[0]].shape[0]
A0 = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}
A1 = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}
self.seebeck = {direction: numpy.nan for direction in self.directions}
self.optic_cond = {direction: numpy.full((n_q,),numpy.nan) for direction in self.directions}
for direction in self.directions:
for iq in xrange(n_q):
A0[direction][iq] = self.transport_coefficient(direction, iq=iq, n=0, beta=beta)
A1[direction][iq] = self.transport_coefficient(direction, iq=iq, n=1, beta=beta)
print "A_0 in direction %s for Omega = %.2f %e a.u." % (direction, self.Om_mesh[iq], A0[direction][iq])
print "A_1 in direction %s for Omega = %.2f %e a.u." % (direction, self.Om_mesh[iq], A1[direction][iq])
if ~numpy.isnan(A1[direction][iq]):
# Seebeck is overwritten if there is more than one Omega = 0 in Om_mesh
self.seebeck[direction] = - A1[direction][iq] / A0[direction][iq] * 86.17
self.optic_cond[direction] = beta * A0[direction] * 10700.0 / numpy.pi
for iq in xrange(n_q):
print "Conductivity in direction %s for Omega = %.2f %f x 10^4 Ohm^-1 cm^-1" % (direction, self.Om_mesh[iq], self.optic_cond[direction][iq])
if not (numpy.isnan(A1[direction][iq])):
print "Seebeck in direction %s for Omega = 0.00 %f x 10^(-6) V/K" % (direction, self.seebeck[direction])
def fermi_dis(self, x):
"""
fermi distribution at x = omega * beta
"""
return 1.0/(numpy.exp(x)+1)
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