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dft_tools/python/sumk_dft.py

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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
import pytriqs.utility.dichotomy as dichotomy
from pytriqs.gf.local import *
import pytriqs.utility.mpi as mpi
from pytriqs.archive import *
from symmetry import *
from sets import Set
from itertools import product
class SumkDFT:
"""This class provides a general SumK method for combining ab-initio code and pytriqs."""
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'):
r"""
Initialises the class from data previously stored into an hdf5 archive.
Parameters
----------
hdf_file : string
Name of hdf5 containing the data.
h_field : scalar, optional
The value of magnetic field to add to the DFT Hamiltonian.
The contribution -h_field*sigma is added to diagonal elements of the Hamiltonian.
It cannot be used with the spin-orbit coupling on; namely h_field is set to 0 if self.SO=True.
use_dft_blocks : boolean, optional
If True, the local Green's function matrix for each spin is divided into smaller blocks
with the block structure determined from the DFT density matrix of the corresponding correlated shell.
dft_data : string, optional
Name of hdf5 subgroup in which DFT data for projector and lattice Green's function construction are stored.
symmcorr_data : string, optional
Name of hdf5 subgroup in which DFT data on symmetries of correlated shells
(symmetry operations, permutaion matrices etc.) are stored.
parproj_data : string, optional
Name of hdf5 subgroup in which DFT data on non-normalized projectors for non-correlated
states (used in the partial density of states calculations) are stored.
symmpar_data : string, optional
Name of hdf5 subgroup in which DFT data on symmetries of the non-normalized projectors
are stored.
bands_data : string, optional
Name of hdf5 subgroup in which DFT data necessary for band-structure/k-resolved spectral
function calculations (projectors, DFT Hamiltonian for a chosen path in the Brillouin zone etc.)
are stored.
transp_data : string, optional
Name of hdf5 subgroup in which DFT data necessary for transport calculations are stored.
misc_data : string, optional
Name of hdf5 subgroup in which miscellaneous DFT data are stored.
"""
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.dft_data = dft_data
self.symmcorr_data = symmcorr_data
self.parproj_data = parproj_data
self.symmpar_data = symmpar_data
self.bands_data = bands_data
self.transp_data = transp_data
self.misc_data = misc_data
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',
'n_inequiv_shells', 'corr_to_inequiv', 'inequiv_to_corr']
self.subgroup_present, self.value_read = self.read_input_from_hdf(subgrp = self.dft_data, things_to_read = things_to_read)
if self.symm_op: self.symmcorr = Symmetry(hdf_file,subgroup=self.symmcorr_data)
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.spin_block_names = [ ['up','down'], ['ud'] ]
self.n_spin_blocks = [2,1]
# Convert spin_block_names to indices -- if spin polarized, differentiate up and down blocks
self.spin_names_to_ind = [{}, {}]
for iso in range(2): # SO = 0 or 1
for isp in range(self.n_spin_blocks[iso]):
self.spin_names_to_ind[iso][self.spin_block_names[iso][isp]] = isp * self.SP
# 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_sumk = [ [ (sp, range( self.corr_shells[icrsh]['dim'])) for sp in self.spin_block_names[self.corr_shells[icrsh]['SO']] ]
for icrsh in range(self.n_corr_shells) ]
# First set a standard gf_struct solver:
self.gf_struct_solver = [ dict([ (sp, range(self.corr_shells[self.inequiv_to_corr[ish]]['dim']) )
for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]]['SO']] ])
for ish in range(self.n_inequiv_shells) ]
# Set standard (identity) maps from gf_struct_sumk <-> gf_struct_solver
self.sumk_to_solver = [ {} for ish in range(self.n_inequiv_shells) ]
self.solver_to_sumk = [ {} for ish in range(self.n_inequiv_shells) ]
self.solver_to_sumk_block = [ {} for ish in range(self.n_inequiv_shells) ]
for ish in range(self.n_inequiv_shells):
for block,inner_list in self.gf_struct_sumk[self.inequiv_to_corr[ish]]:
self.solver_to_sumk_block[ish][block] = block
for inner in inner_list:
self.sumk_to_solver[ish][(block,inner)] = (block,inner)
self.solver_to_sumk[ish][(block,inner)] = (block,inner)
self.deg_shells = [ [] for ish in range(self.n_inequiv_shells) ] # assume no shells are degenerate
self.chemical_potential = 0.0 # initialise mu
self.init_dc() # initialise the double counting
# Analyse the block structure and determine the smallest gf_struct blocks and maps, if desired
if use_dft_blocks: self.analyse_block_structure()
################
# hdf5 FUNCTIONS
################
def read_input_from_hdf(self, subgrp, things_to_read):
r"""
Reads data from the HDF file. Prints a warning if a requested dataset is not found.
Parameters
----------
subgrp : string
Name of hdf5 file subgroup from which the data are to be read.
things_to_read : list of strings
List of datasets to be read from the hdf5 file.
Returns
-------
subgroup_present : boolean
Is the subgrp is present in hdf5 file?
value_read : boolean
Did the reading of requested datasets succeed?
"""
value_read = True
# initialise variables on all nodes to ensure mpi broadcast works at the end
for it in things_to_read: setattr(self,it,0)
subgroup_present = 0
if mpi.is_master_node():
ar = HDFArchive(self.hdf_file,'r')
if subgrp in ar:
subgroup_present = True
# 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)
value_read = False
else:
if (len(things_to_read) != 0): mpi.report("Loading failed: No %s subgroup in hdf5!"%subgrp)
subgroup_present = False
value_read = False
del ar
# now do the broadcasting:
for it in things_to_read: setattr(self,it,mpi.bcast(getattr(self,it)))
subgroup_present = mpi.bcast(subgroup_present)
value_read = mpi.bcast(value_read)
return subgroup_present, value_read
def save(self, things_to_save, subgrp='user_data'):
r"""
Saves data from a list into the HDF file. Prints a warning if a requested data is not found in SumkDFT object.
Parameters
----------
things_to_save : list of strings
List of datasets to be saved into the hdf5 file.
subgrp : string, optional
Name of hdf5 file subgroup in which the data are to be stored.
"""
if not (mpi.is_master_node()): return # do nothing on nodes
ar = HDFArchive(self.hdf_file,'a')
if not subgrp in ar: ar.create_group(subgrp)
for it in things_to_save:
try:
ar[subgrp][it] = getattr(self,it)
except:
mpi.report("%s not found, and so not saved."%it)
del ar
def load(self, things_to_load, subgrp='user_data'):
r"""
Loads user data from the HDF file. Raises an exeption if a requested dataset is not found.
Parameters
----------
things_to_read : list of strings
List of datasets to be read from the hdf5 file.
subgrp : string, optional
Name of hdf5 file subgroup from which the data are to be read.
Returns
-------
list_to_return : list
A list containing data read from hdf5.
"""
if not (mpi.is_master_node()): return # do nothing on nodes
ar = HDFArchive(self.hdf_file,'r')
if not subgrp in ar: mpi.report("Loading %s failed!"%subgrp)
list_to_return = []
for it in things_to_load:
try:
list_to_return.append(ar[subgrp][it])
except:
raise ValueError, "load: %s not found, and so not loaded."%it
del ar
return list_to_return
################
# CORE FUNCTIONS
################
def downfold(self,ik,ish,bname,gf_to_downfold,gf_inp,shells='corr',ir=None):
r"""
Downfolds a block of the Green's function for a given shell and k-point using the corresponding projector matrices.
Parameters
----------
ik : integer
k-point index for which the downfolding is to be done.
ish : integer
Shell index of GF to be downfolded.
- if shells='corr': ish labels all correlated shells (equivalent or not)
- if shells='all': ish labels only representative (inequivalent) non-correlated shells
bname : string
Block name of the target block of the lattice Green's function.
gf_to_downfold : Gf
Block of the Green's function that is to be downfolded.
gf_inp : Gf
FIXME
shells : string, optional
- if shells='corr': orthonormalized projectors for correlated shells are used for the downfolding.
- if shells='all': non-normalized projectors for all included shells are used for the downfolding.
ir : integer, optional
Index of equivalent site in the non-correlated shell 'ish', only used if shells='all'.
Returns
-------
gf_downfolded : Gf
Downfolded block of the lattice Green's function.
"""
gf_downfolded = gf_inp.copy()
isp = self.spin_names_to_ind[self.SO][bname] # get spin index for proj. matrices
n_orb = self.n_orbitals[ik,isp]
if shells == 'corr':
dim = self.corr_shells[ish]['dim']
projmat = self.proj_mat[ik,isp,ish,0:dim,0:n_orb]
elif shells == 'all':
if ir is None: raise ValueError, "downfold: provide ir if treating all shells."
dim = self.shells[ish]['dim']
projmat = self.proj_mat_all[ik,isp,ish,ir,0:dim,0:n_orb]
gf_downfolded.from_L_G_R(projmat,gf_to_downfold,projmat.conjugate().transpose())
return gf_downfolded
def upfold(self,ik,ish,bname,gf_to_upfold,gf_inp,shells='corr',ir=None):
r"""
Upfolds a block of the Green's function for a given shell and k-point using the corresponding projector matrices.
Parameters
----------
ik : integer
k-point index for which the upfolding is to be done.
ish : integer
Shell index of GF to be upfolded.
- if shells='corr': ish labels all correlated shells (equivalent or not)
- if shells='all': ish labels only representative (inequivalent) non-correlated shells
bname : string
Block name of the target block of the lattice Green's function.
gf_to_upfold : Gf
Block of the Green's function that is to be upfolded.
gf_inp : Gf
FIXME
shells : string, optional
- if shells='corr': orthonormalized projectors for correlated shells are used for the upfolding.
- if shells='all': non-normalized projectors for all included shells are used for the upfolding.
ir : integer, optional
Index of equivalent site in the non-correlated shell 'ish', only used if shells='all'.
Returns
-------
gf_upfolded : Gf
Upfolded block of the lattice Green's function.
"""
gf_upfolded = gf_inp.copy()
isp = self.spin_names_to_ind[self.SO][bname] # get spin index for proj. matrices
n_orb = self.n_orbitals[ik,isp]
if shells == 'corr':
dim = self.corr_shells[ish]['dim']
projmat = self.proj_mat[ik,isp,ish,0:dim,0:n_orb]
elif shells == 'all':
if ir is None: raise ValueError, "upfold: provide ir if treating all shells."
dim = self.shells[ish]['dim']
projmat = self.proj_mat_all[ik,isp,ish,ir,0:dim,0:n_orb]
gf_upfolded.from_L_G_R(projmat.conjugate().transpose(),gf_to_upfold,projmat)
return gf_upfolded
def rotloc(self,ish,gf_to_rotate,direction,shells='corr'):
r"""
Rotates a block of the local Green's function from the local frame to the global frame and vice versa.
Parameters
----------
ish : integer
Shell index of GF to be rotated.
- if shells='corr': ish labels all correlated shells (equivalent or not)
- if shells='all': ish labels only representative (inequivalent) non-correlated shells
gf_to_rotate : Gf
Block of the Green's function that is to be rotated.
direction : string
The direction of rotation can be either
- 'toLocal' : global -> local transformation,
- 'toGlobal' : local -> global transformation.
shells : string, optional
- if shells='corr': the rotation matrix for the correlated shell 'ish' is used,
- if shells='all': the rotation matrix for the generic (non-correlated) shell 'ish' is used.
Returns
-------
gf_rotated : Gf
Rotated block of the local Green's function.
"""
assert ((direction == 'toLocal') or (direction == 'toGlobal')),"rotloc: Give direction 'toLocal' or 'toGlobal'."
gf_rotated = gf_to_rotate.copy()
if shells == 'corr':
rot_mat_time_inv = self.rot_mat_time_inv
rot_mat = self.rot_mat
elif shells == 'all':
rot_mat_time_inv = self.rot_mat_all_time_inv
rot_mat = self.rot_mat_all
if direction == 'toGlobal':
if (rot_mat_time_inv[ish] == 1) and self.SO:
gf_rotated << gf_rotated.transpose()
gf_rotated.from_L_G_R(rot_mat[ish].conjugate(),gf_rotated,rot_mat[ish].transpose())
else:
gf_rotated.from_L_G_R(rot_mat[ish],gf_rotated,rot_mat[ish].conjugate().transpose())
elif direction == 'toLocal':
if (rot_mat_time_inv[ish] == 1) and self.SO:
gf_rotated << gf_rotated.transpose()
gf_rotated.from_L_G_R(rot_mat[ish].transpose(),gf_rotated,rot_mat[ish].conjugate())
else:
gf_rotated.from_L_G_R(rot_mat[ish].conjugate().transpose(),gf_rotated,rot_mat[ish])
return gf_rotated
def lattice_gf(self, ik, mu=None, iw_or_w="iw", beta=40, broadening=None, mesh=None, with_Sigma=True, with_dc=True):
r"""
Calculates the lattice Green function for a given k-point from the DFT Hamiltonian and the self energy.
Parameters
----------
ik : integer
k-point index.
mu : real, optional
Chemical potential for which the Green's function is to be calculated.
If not provided, self.chemical_potential is used for mu.
iw_or_w : string, optional
- `iw_or_w` = 'iw' for a imaginary-frequency self-energy
- `iw_or_w` = 'w' for a real-frequency self-energy
beta : real, optional
Inverse temperature.
broadening : real, optional
Imaginary shift for the axis along which the real-axis GF is calculated.
If not provided, broadening will be set to double of the distance between mesh points in 'mesh'.
mesh : list, optional
Data defining mesh on which the real-axis GF will be calculated, given in the form
(om_min,om_max,n_points), where om_min is the minimum omega, om_max is the maximum omega and n_points is the number of points.
with_Sigma : boolean, optional
If True the GF will be calculated with the self-energy stored in self.Sigmaimp_(w/iw), for real/Matsubara GF, respectively.
In this case the mesh is taken from the self.Sigma_imp object.
If with_Sigma=True but self.Sigmaimp_(w/iw) is not present, with_Sigma is reset to False.
with_dc : boolean, optional
if True and with_Sigma=True, the dc correction is substracted from the self-energy before it is included into GF.
Returns
-------
G_latt : BlockGf
Lattice Green's function.
"""
if mu is None: mu = self.chemical_potential
ntoi = self.spin_names_to_ind[self.SO]
spn = self.spin_block_names[self.SO]
if (iw_or_w != "iw") and (iw_or_w != "w"): raise ValueError, "lattice_gf: Implemented only for Re/Im frequency functions."
if not hasattr(self,"Sigma_imp_"+iw_or_w): with_Sigma = False
if broadening is None:
if mesh is None:
broadening = 0.01
else: # broadening = 2 * \Delta omega, where \Delta omega is the spacing of omega points
broadening = 2.0 * ( (mesh[1]-mesh[0])/(mesh[2]-1) )
n_iw = 1025 # Default number of Matsubara frequencies
# Are we including Sigma?
if with_Sigma:
Sigma_imp = getattr(self,"Sigma_imp_"+iw_or_w)
sigma_minus_dc = [s.copy() for s in Sigma_imp]
if with_dc: sigma_minus_dc = self.add_dc(iw_or_w)
if iw_or_w == "iw":
beta = Sigma_imp[0].mesh.beta # override beta if Sigma_iw is present
n_iw = len(Sigma_imp[0].mesh)
else:
if (iw_or_w == "w") and (mesh is None):
raise ValueError, "lattice_gf: Give the mesh=(om_min,om_max,n_points) for the lattice GfReFreq."
# Check if G_latt is present
set_up_G_latt = False # Assume not
if not hasattr(self,"G_latt_"+iw_or_w):
set_up_G_latt = True # Need to create G_latt_(i)w
else: # Check that existing GF is consistent
G_latt = getattr(self,"G_latt_"+iw_or_w)
GFsize = [ gf.N1 for bname,gf in G_latt]
unchangedsize = all( [ self.n_orbitals[ik,ntoi[spn[isp]]]==GFsize[isp] for isp in range(self.n_spin_blocks[self.SO]) ] )
if not unchangedsize: set_up_G_latt = True
if (iw_or_w == "iw") and (self.G_latt_iw.mesh.beta != beta): set_up_G_latt = True # additional check for ImFreq
# Set up G_latt
if set_up_G_latt:
block_structure = [ range(self.n_orbitals[ik,ntoi[sp]]) for sp in spn ]
gf_struct = [ (spn[isp], block_structure[isp]) for isp in range(self.n_spin_blocks[self.SO]) ]
block_ind_list = [block for block,inner in gf_struct]
if iw_or_w == "iw":
glist = lambda : [ GfImFreq(indices=inner,beta=beta,n_points=n_iw) for block,inner in gf_struct]
elif iw_or_w == "w":
if with_Sigma:
glist = lambda : [ GfReFreq(indices=inner,mesh=Sigma_imp[0].mesh) for block,inner in gf_struct]
else:
glist = lambda : [ GfReFreq(indices=inner,window=(mesh[0],mesh[1]),n_points=mesh[2]) for block,inner in gf_struct]
G_latt = BlockGf(name_list = block_ind_list, block_list = glist(), make_copies = False)
G_latt.zero()
if iw_or_w == "iw":
G_latt << iOmega_n
elif iw_or_w == "w":
G_latt << Omega + 1j*broadening
idmat = [numpy.identity(self.n_orbitals[ik,ntoi[sp]],numpy.complex_) for sp in spn]
M = copy.deepcopy(idmat)
for ibl in range(self.n_spin_blocks[self.SO]):
ind = ntoi[spn[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))
G_latt -= M
if with_Sigma:
for icrsh in range(self.n_corr_shells):
for bname,gf in G_latt: gf -= self.upfold(ik,icrsh,bname,sigma_minus_dc[icrsh][bname],gf)
G_latt.invert()
setattr(self,"G_latt_"+iw_or_w,G_latt)
return G_latt
def set_Sigma(self,Sigma_imp):
self.put_Sigma(Sigma_imp)
def put_Sigma(self, Sigma_imp):
r"""
Inserts the impurity self-energies into the sumk_dft class.
Parameters
----------
Sigma_imp : list of BlockGf (Green's function) objects
List containing impurity self-energy for all inequivalent correlated shells.
Self-energies for equivalent shells are then automatically set by this function.
The self-energies can be of the real or imaginary-frequency type.
"""
assert isinstance(Sigma_imp,list), "put_Sigma: 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_shells, "put_Sigma: give exactly one Sigma for each inequivalent corr. shell!"
# init self.Sigma_imp_(i)w:
if all(type(gf) == GfImFreq for bname,gf in Sigma_imp[0]):
# Imaginary frequency Sigma:
self.Sigma_imp_iw = [ BlockGf( name_block_generator = [ (block,GfImFreq(indices = inner, mesh = Sigma_imp[0].mesh))
for block,inner in self.gf_struct_sumk[icrsh] ], make_copies = False)
for icrsh in range(self.n_corr_shells) ]
SK_Sigma_imp = self.Sigma_imp_iw
elif all(type(gf) == GfReFreq for bname,gf in Sigma_imp[0]):
# Real frequency Sigma:
self.Sigma_imp_w = [ BlockGf( name_block_generator = [ (block,GfReFreq(indices = inner, mesh = Sigma_imp[0].mesh))
for block,inner in self.gf_struct_sumk[icrsh] ], make_copies = False)
for icrsh in range(self.n_corr_shells) ]
SK_Sigma_imp = self.Sigma_imp_w
else:
raise ValueError, "put_Sigma: This type of Sigma is not handled."
# transform the CTQMC blocks to the full matrix:
for icrsh in range(self.n_corr_shells):
ish = self.corr_to_inequiv[icrsh] # ish is the index of the inequivalent shell corresponding to icrsh
for block,inner in self.gf_struct_solver[ish].iteritems():
for ind1 in inner:
for ind2 in inner:
block_sumk,ind1_sumk = self.solver_to_sumk[ish][(block,ind1)]
block_sumk,ind2_sumk = self.solver_to_sumk[ish][(block,ind2)]
SK_Sigma_imp[icrsh][block_sumk][ind1_sumk,ind2_sumk] << Sigma_imp[ish][block][ind1,ind2]
# rotation from local to global coordinate system:
if self.use_rotations:
for icrsh in range(self.n_corr_shells):
for bname,gf in SK_Sigma_imp[icrsh]: gf << self.rotloc(icrsh,gf,direction='toGlobal')
def extract_G_loc(self, mu=None, with_Sigma=True, with_dc=True):
r"""
Extracts the local downfolded Green function by the Brillouin-zone integration of the lattice Green's function.
Parameters
----------
mu : real, optional
Input chemical potential. If not provided the value of self.chemical_potential is used as mu.
with_Sigma : boolean, optional
If True then the local GF is calculated with the self-energy self.Sigma_imp.
with_dc : boolean, optional
If True then the double-counting correction is subtracted from the self-energy in calculating the GF.
Returns
-------
G_loc_inequiv : list of BlockGf (Green's function) objects
List of the local Green's functions for all inequivalent correlated shells,
rotated into the corresponding local frames.
"""
if mu is None: mu = self.chemical_potential
G_loc = [ self.Sigma_imp_iw[icrsh].copy() for icrsh in range(self.n_corr_shells) ] # this list will be returned
for icrsh in range(self.n_corr_shells): G_loc[icrsh].zero() # initialize to zero
beta = G_loc[0].mesh.beta
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", with_Sigma=with_Sigma, with_dc=with_dc, beta=beta)
G_latt_iw *= self.bz_weights[ik]
for icrsh in range(self.n_corr_shells):
tmp = G_loc[icrsh].copy() # init temporary storage
for bname,gf in tmp: tmp[bname] << self.downfold(ik,icrsh,bname,G_latt_iw[bname],gf)
G_loc[icrsh] += tmp
# Collect data from mpi
for icrsh in range(self.n_corr_shells):
G_loc[icrsh] << mpi.all_reduce(mpi.world, G_loc[icrsh], lambda x,y : x+y)
mpi.barrier()
# G_loc[:] is now the sum over k projected to the local orbitals.
# here comes the symmetrisation, if needed:
if self.symm_op != 0: G_loc = self.symmcorr.symmetrize(G_loc)
# G_loc is rotated to the local coordinate system:
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')
# transform to CTQMC blocks:
G_loc_inequiv = [ BlockGf( name_block_generator = [ (block,GfImFreq(indices = inner, mesh = G_loc[0].mesh)) for block,inner in self.gf_struct_solver[ish].iteritems() ],
make_copies = False) for ish in range(self.n_inequiv_shells) ]
for ish in range(self.n_inequiv_shells):
for block,inner in self.gf_struct_solver[ish].iteritems():
for ind1 in inner:
for ind2 in inner:
block_sumk,ind1_sumk = self.solver_to_sumk[ish][(block,ind1)]
block_sumk,ind2_sumk = self.solver_to_sumk[ish][(block,ind2)]
G_loc_inequiv[ish][block][ind1,ind2] << G_loc[self.inequiv_to_corr[ish]][block_sumk][ind1_sumk,ind2_sumk]
# return only the inequivalent shells:
return G_loc_inequiv
def analyse_block_structure(self, threshold = 0.00001, include_shells = None, dm = None):
r"""
Determines the block structure of local Green's functions by analysing the structure of
the corresponding density matrices. The resulting block structures for correlated shells
are stored in self.gf_struct_solver list.
Parameters
----------
threshold : real, optional
If the difference between density matrix elements is below threshold,
they are considered to be equal.
include_shells : list of integers, optional
List of correlated shells to be analysed.
If include_shells is not provided all correlated shells will be analysed.
dm : list of dict, optional
List of density matrices from which block stuctures are to be analysed.
Each density matrix is a dict {block names: 2d numpy arrays}.
If not provided, dm will be calculated from the DFT Hamiltonian by a simple-point BZ integration.
"""
self.gf_struct_solver = [ {} for ish in range(self.n_inequiv_shells) ]
self.sumk_to_solver = [ {} for ish in range(self.n_inequiv_shells) ]
self.solver_to_sumk = [ {} for ish in range(self.n_inequiv_shells) ]
self.solver_to_sumk_block = [ {} for ish in range(self.n_inequiv_shells) ]
if dm is None: dm = self.density_matrix(method = 'using_point_integration')
dens_mat = [ dm[self.inequiv_to_corr[ish]] for ish in range(self.n_inequiv_shells) ]
if include_shells is None: include_shells = range(self.n_inequiv_shells)
for ish in include_shells:
for sp in self.spin_block_names[self.corr_shells[self.inequiv_to_corr[ish]]['SO']]:
n_orb = self.corr_shells[self.inequiv_to_corr[ish]]['dim']
dmbool = (abs(dens_mat[ish][sp]) > threshold) # gives an index list of entries larger that threshold
# Determine off-diagonal entries in upper triangular part of density matrix
offdiag = Set([])
for i in range(n_orb):
for j in range(i+1,n_orb):
if dmbool[i,j]: offdiag.add((i,j))
# Determine the number of non-hybridising blocks in the gf
blocs = [ [i] for i in range(n_orb) ]
while len(offdiag) != 0:
pair = offdiag.pop()
for b1,b2 in product(blocs,blocs):
if (pair[0] in b1) and (pair[1] in b2):
if blocs.index(b1) != blocs.index(b2): # In separate blocks?
b1.extend(blocs.pop(blocs.index(b2))) # Merge two blocks
break # Move on to next pair in offdiag
# Set the gf_struct for the solver accordingly
num_blocs = len(blocs)
for i in range(num_blocs):
blocs[i].sort()
self.gf_struct_solver[ish].update( [('%s_%s'%(sp,i),range(len(blocs[i])))] )
# Construct sumk_to_solver taking (sumk_block, sumk_index) --> (solver_block, solver_inner)
# and solver_to_sumk taking (solver_block, solver_inner) --> (sumk_block, sumk_index)
for i in range(num_blocs):
for j in range(len(blocs[i])):
block_sumk = sp
inner_sumk = blocs[i][j]
block_solv = '%s_%s'%(sp,i)
inner_solv = j
self.sumk_to_solver[ish][(block_sumk,inner_sumk)] = (block_solv,inner_solv)
self.solver_to_sumk[ish][(block_solv,inner_solv)] = (block_sumk,inner_sumk)
self.solver_to_sumk_block[ish][block_solv] = block_sumk
# Now calculate degeneracies of orbitals
dm = {}
for block,inner in self.gf_struct_solver[ish].iteritems():
# get dm for the blocks:
dm[block] = numpy.zeros([len(inner),len(inner)],numpy.complex_)
for ind1 in inner:
for ind2 in inner:
block_sumk,ind1_sumk = self.solver_to_sumk[ish][(block,ind1)]
block_sumk,ind2_sumk = self.solver_to_sumk[ish][(block,ind2)]
dm[block][ind1,ind2] = dens_mat[ish][block_sumk][ind1_sumk,ind2_sumk]
for block1 in self.gf_struct_solver[ish].iterkeys():
for block2 in self.gf_struct_solver[ish].iterkeys():
if dm[block1].shape == dm[block2].shape:
if ( (abs(dm[block1] - dm[block2]) < threshold).all() ) and (block1 != block2):
ind1 = -1
ind2 = -2
# check if it was already there:
for n,ind in enumerate(self.deg_shells[ish]):
if block1 in ind: ind1 = n
if block2 in ind: ind2 = n
if (ind1 < 0) and (ind2 >= 0):
self.deg_shells[ish][ind2].append(block1)
elif (ind1 >= 0) and (ind2 < 0):
self.deg_shells[ish][ind1].append(block2)
elif (ind1 < 0) and (ind2 < 0):
self.deg_shells[ish].append([block1,block2])
def density_matrix(self, method = 'using_gf', beta = 40.0):
"""Calculate density matrices in one of two ways.
Parameters
----------
method : string, optional
- if 'using_gf': First get lattice gf (g_loc is not set up), then density matrix.
It is useful for Hubbard I, and very quick.
No assumption on the hopping structure is made (ie diagonal or not).
- if 'using_point_integration': Only works for diagonal hopping matrix (true in wien2k).
beta : float, optional
Inverse temperature.
Returns
-------
dens_mat : list of dicts
Density matrix for each spin in each correlated shell.
"""
dens_mat = [ {} for icrsh in range(self.n_corr_shells)]
for icrsh in range(self.n_corr_shells):
for sp in self.spin_block_names[self.corr_shells[icrsh]['SO']]:
dens_mat[icrsh][sp] = numpy.zeros([self.corr_shells[icrsh]['dim'],self.corr_shells[icrsh]['dim']], numpy.complex_)
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
if method == "using_gf":
G_latt_iw = self.lattice_gf(ik = ik, mu = self.chemical_potential, iw_or_w = "iw", beta = beta)
G_latt_iw *= self.bz_weights[ik]
dm = G_latt_iw.density()
MMat = [dm[sp] for sp in self.spin_block_names[self.SO]]
elif method == "using_point_integration":
ntoi = self.spin_names_to_ind[self.SO]
spn = self.spin_block_names[self.SO]
unchangedsize = all( [self.n_orbitals[ik,ntoi[sp]] == self.n_orbitals[0,ntoi[sp]] for sp in spn] )
if unchangedsize:
dim = self.n_orbitals[0,ntoi[sp]]
else:
dim = self.n_orbitals[ik,ntoi[sp]]
MMat = [numpy.zeros( [dim,dim], numpy.complex_) for sp in spn]
for isp, sp in enumerate(spn):
ind = ntoi[sp]
for inu in range(self.n_orbitals[ik,ind]):
if (self.hopping[ik,ind,inu,inu] - self.h_field*(1-2*isp)) < 0.0: # only works for diagonal hopping matrix (true in wien2k)
MMat[isp][inu,inu] = 1.0
else:
MMat[isp][inu,inu] = 0.0
else: raise ValueError, "density_matrix: the method '%s' is not supported."%method
for icrsh in range(self.n_corr_shells):
for isp, sp in enumerate(self.spin_block_names[self.corr_shells[icrsh]['SO']]):
ind = self.spin_names_to_ind[self.corr_shells[icrsh]['SO']][sp]
dim = self.corr_shells[icrsh]['dim']
n_orb = self.n_orbitals[ik,ind]
projmat = self.proj_mat[ik,ind,icrsh,0:dim,0:n_orb]
if method == "using_gf":
dens_mat[icrsh][sp] += numpy.dot( numpy.dot(projmat,MMat[isp]),
projmat.transpose().conjugate() )
elif method == "using_point_integration":
dens_mat[icrsh][sp] += self.bz_weights[ik] * numpy.dot( numpy.dot(projmat,MMat[isp]) ,
projmat.transpose().conjugate() )
# get data from nodes:
for icrsh in range(self.n_corr_shells):
for sp in dens_mat[icrsh]:
dens_mat[icrsh][sp] = mpi.all_reduce(mpi.world, dens_mat[icrsh][sp], lambda x,y : x+y)
mpi.barrier()
if self.symm_op != 0: dens_mat = self.symmcorr.symmetrize(dens_mat)
# Rotate to local coordinate system:
if self.use_rotations:
for icrsh in range(self.n_corr_shells):
for sp in dens_mat[icrsh]:
if self.rot_mat_time_inv[icrsh] == 1: dens_mat[icrsh][sp] = dens_mat[icrsh][sp].conjugate()
dens_mat[icrsh][sp] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),dens_mat[icrsh][sp]),
self.rot_mat[icrsh] )
return dens_mat
# For simple dft input, get crystal field splittings.
def eff_atomic_levels(self):
r"""
Calculates the effective local Hamiltonian required as an input for
the Hubbard I Solver.
The local Hamiltonian (effective atomic levels) is calculated by
projecting the on-site Bloch Hamiltonian:
.. math:: H^{loc}_{m m'} = \sum_{k} P_{m \nu}(k) H_{\nu\nu'}(k) P^{*}_{\nu' m'}(k),
where
.. math:: H_{\nu\nu'}(k) = [\epsilon_{\nu k} - h_{z} \sigma_{z}] \delta_{\nu\nu'}.
Parameters
----------
None
Returns
-------
eff_atlevels : gf_struct_solver like
Effective local Hamiltonian :math:`H^{loc}_{m m'}` for each correlated shell.
"""
# define matrices for inequivalent shells:
eff_atlevels = [ {} 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']]:
eff_atlevels[ish][sp] = numpy.identity(self.corr_shells[self.inequiv_to_corr[ish]]['dim'], numpy.complex_)
eff_atlevels[ish][sp] *= -self.chemical_potential
eff_atlevels[ish][sp] -= self.dc_imp[self.inequiv_to_corr[ish]][sp]
# 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 icrsh in range(self.n_corr_shells) ]
for icrsh in range(self.n_corr_shells):
dim = self.corr_shells[icrsh]['dim']
for sp in self.spin_block_names[self.corr_shells[icrsh]['SO']]:
self.Hsumk[icrsh][sp] = numpy.zeros([dim,dim],numpy.complex_)
for isp, sp in enumerate(self.spin_block_names[self.corr_shells[icrsh]['SO']]):
ind = self.spin_names_to_ind[self.corr_shells[icrsh]['SO']][sp]
for ik in range(self.n_k):
n_orb = self.n_orbitals[ik,ind]
MMat = numpy.identity(n_orb, numpy.complex_)
MMat = self.hopping[ik,ind,0:n_orb,0:n_orb] - (1-2*isp) * self.h_field * MMat
projmat = self.proj_mat[ik,ind,icrsh,0:dim,0:n_orb]
self.Hsumk[icrsh][sp] += self.bz_weights[ik] * numpy.dot( numpy.dot(projmat,MMat),
projmat.conjugate().transpose() )
# symmetrisation:
if self.symm_op != 0: self.Hsumk = self.symmcorr.symmetrize(self.Hsumk)
# Rotate to local coordinate system:
if self.use_rotations:
for icrsh in range(self.n_corr_shells):
for sp in self.Hsumk[icrsh]:
if self.rot_mat_time_inv[icrsh] == 1: self.Hsumk[icrsh][sp] = self.Hsumk[icrsh][sp].conjugate()
self.Hsumk[icrsh][sp] = numpy.dot( numpy.dot(self.rot_mat[icrsh].conjugate().transpose(),self.Hsumk[icrsh][sp]) ,
self.rot_mat[icrsh] )
# add to matrix:
for ish in range(self.n_inequiv_shells):
for sp in eff_atlevels[ish]:
eff_atlevels[ish][sp] += self.Hsumk[self.inequiv_to_corr[ish]][sp]
return eff_atlevels
def init_dc(self):
r"""
Initializes the double counting terms.
Parameters
----------
None
"""
self.dc_imp = [ {} for icrsh in range(self.n_corr_shells)]
for icrsh in range(self.n_corr_shells):
dim = self.corr_shells[icrsh]['dim']
spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
for sp in spn: self.dc_imp[icrsh][sp] = numpy.zeros([dim,dim],numpy.float_)
self.dc_energ = [0.0 for icrsh in range(self.n_corr_shells)]
def set_dc(self,dc_imp,dc_energ):
r"""
Sets double counting corrections to given values.
Parameters
----------
dc_imp : gf_struct_sumk like
Double-counting self-energy term.
dc_energ : list of floats
Double-counting energy corrections for each correlated shell.
"""
self.dc_imp = dc_imp
self.dc_energ = dc_energ
def calc_dc(self,dens_mat,orb=0,U_interact=None,J_hund=None,use_dc_formula=0,use_dc_value=None):
r"""
Calculates and sets the double counting corrections.
If 'use_dc_value' is provided the double-counting term is uniformly initialized
with this constant and 'U_interact' and 'J_hund' are ignored.
If 'use_dc_value' is None the correction is evaluated according to
one of the following formulae:
* use_dc_formula = 0: fully-localised limit (FLL)
* use_dc_formula = 1: Held's formula, i.e. mean-field formula for the Kanamori
type of the interaction Hamiltonian
* use_dc_formula = 2: around mean-field (AMF)
Note that FLL and AMF formulae were derived assuming a full Slater-type interaction
term and should be thus used accordingly. For the Kanamori-type interaction
one should use formula 1.
The double-counting self-energy term is stored in `self.dc_imp` and the energy
correction in `self.dc_energ`.
Parameters
----------
dens_mat : gf_struct_solver like
Density matrix for the specified correlated shell.
orb : int, optional
Index of an inequivalent shell.
U_interact : float, optional
Value of interaction parameter `U`.
J_hund : float, optional
Value of interaction parameter `J`.
use_dc_formula : int, optional
Type of double-counting correction (see description).
use_dc_value : float, optional
Value of the double-counting correction. If specified
`U_interact`, `J_hund` and `use_dc_formula` are ignored.
"""
for icrsh in range(self.n_corr_shells):
ish = self.corr_to_inequiv[icrsh] # ish is the index of the inequivalent shell corresponding to icrsh
if ish != orb: continue # ignore this orbital
dim = self.corr_shells[icrsh]['dim'] #*(1+self.corr_shells[icrsh]['SO'])
spn = self.spin_block_names[self.corr_shells[icrsh]['SO']]
Ncr = { sp: 0.0 for sp in spn }
for block,inner in self.gf_struct_solver[ish].iteritems():
bl = self.solver_to_sumk_block[ish][block]
Ncr[bl] += dens_mat[block].real.trace()
Ncrtot = sum(Ncr.itervalues())
for sp in spn:
self.dc_imp[icrsh][sp] = numpy.identity(dim,numpy.float_)
if self.SP == 0: # average the densities if there is no SP:
Ncr[sp] = Ncrtot / len(spn)
elif self.SP == 1 and self.SO == 1: # correction for SO: we have only one block in this case, but in DC we need N/2
Ncr[sp] = Ncrtot / 2.0
if use_dc_value is None:
if U_interact is None and J_hund is None: raise ValueError, "set_dc: either provide U_interact and J_hund or set use_dc_value to dc value."
if use_dc_formula == 0: # FLL
self.dc_energ[icrsh] = U_interact / 2.0 * Ncrtot * (Ncrtot-1.0)
for sp in spn:
Uav = U_interact*(Ncrtot-0.5) - J_hund*(Ncr[sp] - 0.5)
self.dc_imp[icrsh][sp] *= Uav
self.dc_energ[icrsh] -= J_hund / 2.0 * (Ncr[sp]) * (Ncr[sp]-1.0)
mpi.report("DC for shell %(icrsh)i and block %(sp)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 + (dim-1)*(U_interact-2.0*J_hund) + (dim-1)*(U_interact-3.0*J_hund))/(2*dim-1) / 2.0 * Ncrtot * (Ncrtot-1.0)
for sp in spn:
Uav =(U_interact + (dim-1)*(U_interact-2.0*J_hund) + (dim-1)*(U_interact-3.0*J_hund))/(2*dim-1) * (Ncrtot-0.5)
self.dc_imp[icrsh][sp] *= Uav
mpi.report("DC for shell %(icrsh)i and block %(sp)s = %(Uav)f"%locals())
elif use_dc_formula == 2: # AMF
self.dc_energ[icrsh] = 0.5 * U_interact * Ncrtot * Ncrtot
for sp in spn:
Uav = U_interact*(Ncrtot - Ncr[sp]/dim) - J_hund * (Ncr[sp] - Ncr[sp]/dim)
self.dc_imp[icrsh][sp] *= Uav
self.dc_energ[icrsh] -= (U_interact + (dim-1)*J_hund)/dim * 0.5 * Ncr[sp] * Ncr[sp]
mpi.report("DC for shell %(icrsh)i and block %(sp)s = %(Uav)f"%locals())
mpi.report("DC energy for shell %s = %s"%(icrsh,self.dc_energ[icrsh]))
else: # use value provided for user to determine dc_energ and dc_imp
self.dc_energ[icrsh] = use_dc_value * Ncrtot
for sp in spn: self.dc_imp[icrsh][sp] *= use_dc_value
mpi.report("DC for shell %(icrsh)i = %(use_dc_value)f"%locals())
mpi.report("DC energy = %s"%self.dc_energ[icrsh])
def add_dc(self,iw_or_w="iw"):
r"""
Subtracts the double counting term from the impurity self energy.
Parameters
----------
iw_or_w : string, optional
- `iw_or_w` = 'iw' for a imaginary-frequency self-energy
- `iw_or_w` = 'w' for a real-frequency self-energy
Returns
-------
sigma_minus_dc : gf_struct_sumk like
Self-energy with a subtracted double-counting term.
"""
# Be careful: Sigma_imp is already in the global coordinate system!!
sigma_minus_dc = [s.copy() for s in getattr(self,"Sigma_imp_"+iw_or_w)]
for icrsh in range(self.n_corr_shells):
for bname,gf in sigma_minus_dc[icrsh]:
# Transform dc_imp to global coordinate system
dccont = numpy.dot(self.rot_mat[icrsh],numpy.dot(self.dc_imp[icrsh][bname],self.rot_mat[icrsh].conjugate().transpose()))
sigma_minus_dc[icrsh][bname] -= dccont
return sigma_minus_dc
def symm_deg_gf(self,gf_to_symm,orb):
r"""
Averages a GF over degenerate shells.
Degenerate shells of an inequivalent correlated shell are defined by
`self.deg_shells`. This function enforces corresponding degeneracies
in the input GF.
Parameters
----------
gf_to_symm : gf_struct_solver like
Input GF.
orb : int
Index of an inequivalent shell.
"""
for degsh in self.deg_shells[orb]:
ss = gf_to_symm[degsh[0]].copy()
ss.zero()
n_deg = len(degsh)
for bl in degsh: ss += gf_to_symm[bl] / (1.0*n_deg)
for bl in degsh: gf_to_symm[bl] << ss
def total_density(self, mu=None, with_Sigma=True, with_dc=True):
r"""
Calculates the total charge within the energy window for a given chemical potential.
The chemical potential is either given by parameter `mu` or, if it is not specified,
taken from `self.chemical_potential`.
The total charge is calculated from the trace of the GF in the Bloch basis.
By deafult, a full interacting GF is used. To use the non-interacting GF, set
parameter `with_Sigma = False`.
The number of bands within the energy windows generally depends on `k`. The trace is
therefore calculated separately for each `k`-point.
Since in general n_orbitals depends on k, the calculation is done in the following order:
..math:: n_{tot} = \sum_{k} n(k),
with
..math:: n(k) = Tr G_{\nu\nu'}(k, i\omega_{n}).
The calculation is done in the global coordinate system, if distinction is made between local/global.
Parameters
----------
mu : float, optional
Input chemical potential. If not specified, `self.chemical_potential` is used instead.
with_Sigma : boolean, optional
If `True` the full interacing GF is evaluated, otherwise the self-energy is not
included and the charge would correspond to a non-interacting system.
with_dc : boolean, optional
Whether or not to subtract the double-counting term from the self-energy.
Returns
-------
dens : float
Total charge :math:`n_{tot}`.
"""
if mu is None: mu = self.chemical_potential
dens = 0.0
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", with_Sigma=with_Sigma, with_dc=with_dc)
dens += self.bz_weights[ik] * G_latt_iw.total_density()
# collect data from mpi:
dens = mpi.all_reduce(mpi.world, dens, lambda x,y : x+y)
mpi.barrier()
return dens
def set_mu(self,mu):
r"""
Sets a new chemical potential.
Parameters
----------
mu : float
New value of the chemical potential.
"""
self.chemical_potential = mu
def calc_mu(self, precision=0.01):
r"""
Searches for the chemical potential that gives the DFT total charge.
A simple bisection method is used.
Parameters
----------
precision : float, optional
A desired precision of the resulting total charge.
Returns
-------
mu : float
Value of the chemical potential giving the DFT total charge
within specified precision.
"""
F = lambda mu : self.total_density(mu=mu)
density = self.density_required - self.charge_below
self.chemical_potential = dichotomy.dichotomy(function = F,
x_init = self.chemical_potential, y_value = density,
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 calc_density_correction(self, filename='dens_mat.dat'):
r"""
Calculates the charge density correction and stores it into a file.
The charge density correction is needed for charge-self-consistent DFT+DMFT calculations.
It represents a density matrix of the interacting system defined in Bloch basis
and it is calculated from the sum over Matsubara frequecies of the full GF,
..math:: N_{\nu\nu'}(k) = \sum_{i\omega_{n}} G_{\nu\nu'}(k, i\omega_{n})
The density matrix for every `k`-point is stored into a file.
Parameters
----------
filename : string
Name of the file to store the charge density correction.
Returns
-------
(deltaN, dens) : tuple
Returns a tuple containing the density matrix `deltaN` and
the corresponing total charge `dens`.
"""
assert type(filename) == StringType, "calc_density_correction: filename has to be a string!"
ntoi = self.spin_names_to_ind[self.SO]
spn = self.spin_block_names[self.SO]
dens = {sp: 0.0 for sp in spn}
# Set up deltaN:
deltaN = {}
for sp in spn:
deltaN[sp] = [numpy.zeros([self.n_orbitals[ik,ntoi[sp]],self.n_orbitals[ik,ntoi[sp]]], numpy.complex_) for ik in range(self.n_k)]
ikarray = numpy.array(range(self.n_k))
for ik in mpi.slice_array(ikarray):
G_latt_iw = self.lattice_gf(ik = ik, mu = self.chemical_potential, iw_or_w = "iw")
for bname,gf in G_latt_iw:
deltaN[bname][ik] = G_latt_iw[bname].density()
dens[bname] += self.bz_weights[ik] * G_latt_iw[bname].total_density()
# mpi reduce:
for bname in deltaN:
for ik in range(self.n_k):
deltaN[bname][ik] = mpi.all_reduce(mpi.world, deltaN[bname][ik], lambda x,y : x+y)
dens[bname] = mpi.all_reduce(mpi.world, dens[bname], 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 rydberg-1
f.write("%.14f\n"%(G_latt_iw.mesh.beta*self.energy_unit))
if self.SP != 0: f1.write("%.14f\n"%(G_latt_iw.mesh.beta*self.energy_unit))
if self.SP == 0: # no spin-polarization
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: # with spin-polarization
# dict of filename: (spin index, block_name)
if self.SO == 0: to_write = {f: (0, 'up'), f1: (1, 'down')}
if self.SO == 1: to_write = {f: (0, 'ud'), f1: (0, 'ud')}
for fout in to_write.iterkeys():
isp, sp = to_write[fout]
for ik in range(self.n_k):
fout.write("%s\n"%self.n_orbitals[ik,isp])
for inu in range(self.n_orbitals[ik,isp]):
for imu in range(self.n_orbitals[ik,isp]):
fout.write("%.14f %.14f "%(deltaN[sp][ik][inu,imu].real,deltaN[sp][ik][inu,imu].imag))
fout.write("\n")
fout.write("\n")
fout.close()
return deltaN, dens
################
# FIXME LEAVE UNDOCUMENTED
################
def calc_dc_for_density(self,orb,dc_init,dens_mat,density=None,precision=0.01):
"""Searches for DC in order to fulfill charge neutrality.
If density is given, then DC is set such that the LOCAL charge of orbital
orb coincides with the given density."""
def F(dc):
self.calc_dc(dens_mat = dens_mat, U_interact = 0, J_hund = 0, orb = orb, use_dc_value = dc)
if dens_req is None:
return self.total_density(mu = mu)
else:
return self.extract_G_loc()[orb].total_density()
if density is None: density = self.density_required - self.charge_below
dc = dichotomy.dichotomy(function = F,
x_init = dc_init, y_value = density,
precision_on_y = precision, delta_x = 0.5,
max_loops = 100, x_name = "Double Counting", y_name= "Total Density",
verbosity = 3)[0]
return dc
def check_projectors(self):
"""Calculated the density matrix from projectors (DM = P Pdagger) to check that it is correct and
specifically that it matches DFT."""
dens_mat = [numpy.zeros([self.corr_shells[icrsh]['dim'],self.corr_shells[icrsh]['dim']],numpy.complex_)
for icrsh in range(self.n_corr_shells)]
for ik in range(self.n_k):
for icrsh in range(self.n_corr_shells):
dim = self.corr_shells[icrsh]['dim']
n_orb = self.n_orbitals[ik,0]
projmat = self.proj_mat[ik,0,icrsh,0:dim,0:n_orb]
dens_mat[icrsh][:,:] += numpy.dot(projmat, projmat.transpose().conjugate()) * self.bz_weights[ik]
if self.symm_op != 0: dens_mat = self.symmcorr.symmetrize(dens_mat)
# Rotate to local coordinate system:
if self.use_rotations:
for icrsh in range(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 sorts_of_atoms(self,shells):
"""
Determine the number of inequivalent sorts.
"""
sortlst = [ shells[i]['sort'] for i in range(len(shells)) ]
n_sorts = len(set(sortlst))
return n_sorts
def number_of_atoms(self,shells):
"""
Determine the number of inequivalent atoms.
"""
atomlst = [ shells[i]['atom'] for i in range(len(shells)) ]
n_atoms = len(set(atomlst))
return n_atoms
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