mirror of https://github.com/triqs/dft_tools
108 lines
4.0 KiB
Python
108 lines
4.0 KiB
Python
##########################################################################
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#
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# TRIQS: a Toolbox for Research in Interacting Quantum Systems
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#
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# Copyright (C) 2023 by A. Carta, A. Hampel
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#
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# TRIQS is free software: you can redistribute it and/or modify it under the
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# terms of the GNU General Public License as published by the Free Software
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# Foundation, either version 3 of the License, or (at your option) any later
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# version.
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#
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# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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# details.
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#
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# You should have received a copy of the GNU General Public License along with
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# TRIQS. If not, see <http://www.gnu.org/licenses/>.
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#
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##########################################################################
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import numpy as np
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import triqs.utility.mpi as mpi
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def compute_DC_from_density(N_tot, U, J, N_spin=None, n_orbitals=5, method='sFLL'):
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"""
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Computes the double counting correction using various methods.
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For FLL and AMF DC the notations and equations from doi.org/10.1038/s41598-018-27731-4
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are used, whereas for the Held DC the definitions from doi.org/10.1080/00018730701619647 are used.
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Parameters
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----------
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N_tot : float
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Total density of the impurity
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N_spin : float , default = None
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Spin density, defaults to N_tot*0.5 if not specified
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U : float
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U value
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J : float
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J value
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n_orbitals : int, default = 5
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Total number of orbitals
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method : string, default = 'cFLL'
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possibilities:
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- cFLL: DC potential from Ryee for spin unpolarized DFT: (DOI: 10.1038/s41598-018-27731-4)
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- sFLL: same as above for spin polarized DFT
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- cAMF: around mean field
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- sAMF: spin polarized around mean field
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- cHeld: unpolarized Held's formula as reported in (DOI: 10.1103/PhysRevResearch.2.03308)
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- sHeld: NOT IMPLEMENTED
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Returns
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-------
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List of floats:
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- DC_val: double counting potential
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- E_val: double counting energy
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todo:
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- See whether to move this to TRIQS directly instead of dft_tools
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- allow as input full density matrix to allow orbital dependent DC
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"""
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if N_spin is not None:
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N_spin2 = N_tot-N_spin
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Mag = N_spin - N_spin2
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L_orbit = (n_orbitals-1)/2
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if method == 'cFLL':
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E_val = 0.5 * U * N_tot * (N_tot-1) - 0.5 * J * N_tot * (N_tot*0.5-1)
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DC_val = U * (N_tot-0.5) - J * (N_tot*0.5-0.5)
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elif method == 'sFLL':
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assert N_spin is not None, "Spin density not given"
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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
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DC_val = U * (N_tot-0.5) - J * (N_spin-0.5)
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elif method == 'cAMF':
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E_val = +0.5 * U * N_tot ** 2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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DC_val = U * N_tot - 0.5*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot
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elif method == 'sAMF':
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assert N_spin is not None, "Spin density not given"
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E_val = 0.5 * U * N_tot ** 2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*N_tot**2
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E_val -= 0.25*(U+2*L_orbit*J)/(2*L_orbit+1)*Mag**2
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DC_val = U * N_tot - (U+2*L_orbit*J)/(2*L_orbit+1)*N_spin
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elif method == 'cHeld':
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# Valid for a Kanamori-type Hamiltonian where U'=U-2J
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U_mean = (U + (n_orbitals-1)*(U-2*J)+(n_orbitals-1)*(U-3*J))/(2*n_orbitals-1)
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E_val = 0.5 * U_mean * N_tot * (N_tot - 1)
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DC_val = U_mean * (N_tot-0.5)
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elif method == 'sHeld':
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raise ValueError(f"Method sHeld not yet implemented")
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else:
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raise ValueError(f"DC type {method} not supported")
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mpi.report(f"DC potential computed using the {method} method, V_DC = {DC_val:.6f} eV")
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mpi.report(f"E_DC using the {method} method, E_DC = {E_val:.6f} eV")
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if 'Held' in method:
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mpi.report(f"Held method for {n_orbitals} orbitals, computed U_mean={U_mean:.6f} eV")
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return DC_val, E_val
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