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outsource calc_DC_from_density into util.py and cleanup

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Alexander Hampel 2023-03-20 10:01:44 -04:00
parent 0d25aefc73
commit 88094c0f92
3 changed files with 112 additions and 85 deletions
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83
python/triqs_dft_tools/sumk_dft.py
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@ -33,93 +33,12 @@ from triqs.utility.comparison_tests import assert_arrays_are_close
from h5 import *
from .symmetry import *
from .block_structure import BlockStructure
from .util import compute_DC_from_density
from itertools import product
from warnings import warn
from scipy import compress
from scipy.optimize import minimize, newton, brenth
def compute_DC_from_density(N_tot, U, J, N_spin = None, n_orbitals=5, method='sFLL'):
"""
Computes the double counting correction using various methods.
For FLL and AMF DC the notations and equations from doi.org/10.1038/s41598-018-27731-4
are used, whereas for the Held DC the definitions from doi.org/10.1080/00018730701619647 are used.
Parameters
----------
N_tot : float
Total density of the impurity
N_spin : float , default = None
Spin density, defaults to N_tot*0.5 if not specified
U : float
U value
J : float
J value
n_orbitals : int, default = 5
Total number of orbitals
method : string, default = 'cFLL'
possibilities:
- cFLL: DC potential from Ryee for spin unpolarized DFT: (DOI: 10.1038/s41598-018-27731-4)
- sFLL: same as above for spin polarized DFT
- cAMF: around mean field
- sAMF: spin polarized around mean field
- cHeld: unpolarized Held's formula as reported in (DOI: 10.1103/PhysRevResearch.2.03308)
- sHeld: NOT IMPLEMENTED
Returns
-------
List of floats:
- DC_val: double counting potential
- E_val: double counting energy
todo: See whether to move this to TRIQS directly instead of dft_tools
"""
if N_spin is not None:
N_spin2 = N_tot-N_spin
Mag = N_spin - N_spin2
L_orbit = (n_orbitals-1)/2
if method == 'cFLL':
E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
DC_val = U * (N_tot-0.5) - J *(N_tot*0.5-0.5)
elif method == 'sFLL':
assert N_spin is not None, "Spin density not given"
E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1) - 0.25 * J * Mag**2
DC_val = U * (N_tot-0.5) - J *(N_spin-0.5)
elif method == 'cAMF':
E_val = +0.5 * U * N_tot **2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
elif method == 'sAMF':
assert N_spin is not None, "Spin density not given"
E_val = 0.5 * U * N_tot **2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
elif method == 'cHeld':
# Valid for a Kanamori-type Hamiltonian where U'=U-2J
U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
DC_val = U_mean * (N_tot-0.5)
elif method == 'sHeld':
raise ValueError(f"Method sHeld not yet implemented")
else:
raise ValueError(f"DC type {method} not supported")
mpi.report(f"DC potential computed using the {method} method, V_DC = {DC_val:.6f} eV")
mpi.report(f"E_DC using the {method} method, E_DC = {E_val:.6f} eV")
if 'Held' in method:
mpi.report(f"Held method for {n_orbitals} orbitals, computed U_mean={U_mean:.6f} eV")
return DC_val, E_val
class SumkDFT(object):
"""This class provides a general SumK method for combining ab-initio code and triqs."""

107
python/triqs_dft_tools/util.py Normal file
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@ -0,0 +1,107 @@
##########################################################################
#
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
#
# Copyright (C) 2023 by A. Carta, A. Hampel
#
# 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/>.
#
##########################################################################
import numpy as np
import triqs.utility.mpi as mpi
def compute_DC_from_density(N_tot, U, J, N_spin=None, n_orbitals=5, method='sFLL'):
"""
Computes the double counting correction using various methods.
For FLL and AMF DC the notations and equations from doi.org/10.1038/s41598-018-27731-4
are used, whereas for the Held DC the definitions from doi.org/10.1080/00018730701619647 are used.
Parameters
----------
N_tot : float
Total density of the impurity
N_spin : float , default = None
Spin density, defaults to N_tot*0.5 if not specified
U : float
U value
J : float
J value
n_orbitals : int, default = 5
Total number of orbitals
method : string, default = 'cFLL'
possibilities:
- cFLL: DC potential from Ryee for spin unpolarized DFT: (DOI: 10.1038/s41598-018-27731-4)
- sFLL: same as above for spin polarized DFT
- cAMF: around mean field
- sAMF: spin polarized around mean field
- cHeld: unpolarized Held's formula as reported in (DOI: 10.1103/PhysRevResearch.2.03308)
- sHeld: NOT IMPLEMENTED
Returns
-------
List of floats:
- DC_val: double counting potential
- E_val: double counting energy
todo:
- See whether to move this to TRIQS directly instead of dft_tools
- allow as input full density matrix to allow orbital dependent DC
"""
if N_spin is not None:
N_spin2 = N_tot-N_spin
Mag = N_spin - N_spin2
L_orbit = (n_orbitals-1)/2
if method == 'cFLL':
E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
DC_val = U * (N_tot-0.5) - J * (N_tot*0.5-0.5)
elif method == 'sFLL':
assert N_spin is not None, "Spin density not given"
E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1) - 0.25 * J * Mag**2
DC_val = U * (N_tot-0.5) - J * (N_spin-0.5)
elif method == 'cAMF':
E_val = +0.5 * U * N_tot ** 2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
elif method == 'sAMF':
assert N_spin is not None, "Spin density not given"
E_val = 0.5 * U * N_tot ** 2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
elif method == 'cHeld':
# Valid for a Kanamori-type Hamiltonian where U'=U-2J
U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
DC_val = U_mean * (N_tot-0.5)
elif method == 'sHeld':
raise ValueError(f"Method sHeld not yet implemented")
else:
raise ValueError(f"DC type {method} not supported")
mpi.report(f"DC potential computed using the {method} method, V_DC = {DC_val:.6f} eV")
mpi.report(f"E_DC using the {method} method, E_DC = {E_val:.6f} eV")
if 'Held' in method:
mpi.report(f"Held method for {n_orbitals} orbitals, computed U_mean={U_mean:.6f} eV")
return DC_val, E_val

7
test/python/dc_test.py
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@ -23,6 +23,7 @@
import numpy as np
from triqs_dft_tools.sumk_dft import *
from triqs_dft_tools.util import compute_DC_from_density
from triqs.gf import *
from h5 import HDFArchive
from triqs.operators.util import *
@ -50,7 +51,7 @@ method_dict = {
def test_dc(method, method_dict, dens, Uval, Jval, filename):
def test_dc(SK_compat, SK_new, method, method_dict, dens, Uval, Jval, filename):
dc_no = method_dict[method]["numbering_convention"]
dc_string = method_dict[method]["new_convention"]
@ -117,7 +118,7 @@ N_tot = N_up + N_down
mpi.report(f"{N_up=} ,{N_down=}, {N_tot=}\n")
for method in ["FLL", "AMF", "Held"]:
test_dc(method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5")
test_dc(SK_compat, SK_new, method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5")
#in case implementation changes, to write new testing data into archive
#R = HDFArchive('./NiO.ref.h5', 'a')
@ -158,7 +159,7 @@ Uval = 5
Jval = 0.3
for method in ["FLL", "AMF", "Held"]:
test_dc(method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5" )
test_dc(SK_compat, SK_new, method, method_dict, dens, Uval, Jval, filename = f"{dft_filename}.h5" )
#in case implementation changes, to write new testing data into archive
#R = HDFArchive(f'./{dft_filename}.h5', 'a')