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https://github.com/triqs/dft_tools
synced 2024-12-22 20:34:38 +01:00
fix: velocities from WannierBerri now correctly implemented
fix: transport function not implemented if using symmetries feat: computing OC in Wannier or Hamiltonian basis feat: computing intra- and interband contributions separately in OC
This commit is contained in:
phibeck
Alexander Hampel
parent
d5e6d60258
commit
e949d4c1b0
@ -21,6 +21,7 @@
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##########################################################################
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import sys
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import numpy
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from warnings import warn
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from triqs.gf import *
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import triqs.utility.mpi as mpi
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from .symmetry import *
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@ -175,7 +176,7 @@ def fermi_dis(w, beta, der=0):
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else:
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raise('higher order of derivative than 1 not implemented')
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def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='./', calc_velocity=False, calc_inverse_mass=False):
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def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='./', calc_velocity=False, calc_inverse_mass=False, oc_select='both', oc_basis='h'):
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r"""
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Recomputes dft_input objects on a finer mesh using WannierBerri and Wannier90 input.
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@ -196,6 +197,10 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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whether the velocity (first derivative of H(k)) is computed
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calc_inverse_mass : boolean, optional, default=False
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whether the inverse effective mass (second derivative of H(k)) is computed
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oc_select : string, optional, default='both'
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select contributions for optical conductivity from ['intra', 'inter', 'both']
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oc_basis : string, optional, default='h'
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gauge choice options 'h' for Hamiltonian/band and 'w' for Wannier basis
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Returns
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-------
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@ -205,6 +210,8 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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dictionary of datasets to be temporarily overwritten
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"""
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mpi.report('Starting Wannier interpolation...')
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BOHRTOANG = cst.physical_constants['Bohr radius'][0]/cst.angstrom
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HARTREETOEV = cst.physical_constants['Hartree energy'][0]/cst.eV
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n_inequiv_spin_blocks = sum_k.SP + 1 - sum_k.SO
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@ -259,19 +266,68 @@ def recompute_w90_input_on_different_mesh(sum_k, seedname, nk_optics, pathname='
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dataK = wb.data_K.Data_K(wberri, dK=shift_gamma, grid=grid, fftlib='numpy')
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# read in hoppings and proj_mat
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hopping[:,0,range(hopping.shape[2]),range(hopping.shape[3])] = dataK.E_K
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if oc_basis == 'h':
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hopping[:,0,range(hopping.shape[2]),range(hopping.shape[3])] = dataK.E_K
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elif oc_basis == 'w':
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hopping[:,0,:,:] = dataK.HH_K
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fake_proj_mat = numpy.zeros(numpy.shape(dataK.UU_K), dtype=complex)
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fake_proj_mat[:,range(numpy.shape(fake_proj_mat)[1]),range(numpy.shape(fake_proj_mat)[2])] = 1. + 1j*0.0
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for isp in range(n_inequiv_spin_blocks):
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iorb = 0
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for icrsh in range(sum_k.n_corr_shells):
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dim = sum_k.corr_shells[icrsh]['dim']
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proj_mat[:,isp,icrsh,0:dim,:] = dataK.UU_K[:,iorb:iorb+dim,:]
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if oc_basis == 'h':
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proj_mat[:,isp,icrsh,0:dim,:] = dataK.UU_K[:,iorb:iorb+dim,:]
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elif oc_basis == 'w':
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proj_mat[:,isp,icrsh,0:dim,:] = fake_proj_mat[:,iorb:iorb+dim,:]
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iorb += dim
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if calc_velocity:
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# construct velocities from dataK
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V_H_diag = numpy.zeros(numpy.shape(dataK.Xbar('Ham', 1)), dtype=complex)
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V_H_diag[:, range(V_H_diag.shape[1]), range(V_H_diag.shape[1]), :] = numpy.einsum('knna -> kna', dataK.Xbar('Ham', 1))
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velocities_k = ( V_H_diag - dataK.Xbar('AA') * 1j*( dataK.E_K[:,None,:,None] - dataK.E_K[:,:,None,None] ) ) / HARTREETOEV / BOHRTOANG
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# velocity: [k x n_orb x n_orb x R]
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def _commutator(A, B):
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term1 = numpy.einsum('kmo, kona -> kmna', A, B)
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term2 = numpy.einsum('kmoa, kon -> kmna', B, A)
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return term1 - term2
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# in the band basis
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# vh_alpha = Hhbar_alpha + i [Hh, Ahbar_alpha]
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if oc_basis == 'h':
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# first term
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Hhbar_alpha = dataK.Xbar('Ham', 1)
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# second term
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c_Hh_Ahbar_alpha = _commutator(hopping[:,0,:,:], dataK.Xbar('AA'))
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velocities_k = (Hhbar_alpha + 1j * c_Hh_Ahbar_alpha) / HARTREETOEV / BOHRTOANG
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# split into diag and offdiag elements, corresponding to intra- and interband contributions
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v_diag = numpy.zeros(numpy.shape(velocities_k), dtype=complex)
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v_diag[:,range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]),:] = velocities_k[:,range(numpy.shape(velocities_k)[1]),
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range(numpy.shape(velocities_k)[2]),:]
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v_offdiag = velocities_k.copy()
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v_offdiag[:,range(numpy.shape(velocities_k)[1]),range(numpy.shape(velocities_k)[2]),:] = 0. + 1j*0.0
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if oc_select == 'intra':
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velocities_k = v_diag
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elif oc_select == 'inter':
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velocities_k = v_offdiag
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elif oc_select == 'both':
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velocities_k = v_diag + v_offdiag
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# in the orbital basis
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# vw_alpha = Hw_alpha + i [Hw, Aw_alpha]
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elif oc_basis == 'w':
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# first term
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Hw_alpha_R = dataK.Ham_R.copy()
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for i in range(1):
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shape_cR = numpy.shape(dataK.cRvec_wcc)
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Hw_alpha_R = 1j * Hw_alpha_R.reshape((Hw_alpha_R.shape) + (1, )) * dataK.cRvec_wcc.reshape(
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(shape_cR[0], shape_cR[1], dataK.system.nRvec) + (1, ) * len(Hw_alpha_R.shape[3:]) + (3, ))
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Hw_alpha = dataK.fft_R_to_k(Hw_alpha_R, hermitean=False)[dataK.select_K]
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# second term
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Aw_alpha = dataK.fft_R_to_k(dataK.AA_R, hermitean=True)
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c_Hw_Aw_alpha = _commutator(hopping[:,0,:,:], Aw_alpha)
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velocities_k = (Hw_alpha + 1j * c_Hw_Aw_alpha) / HARTREETOEV / BOHRTOANG
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if calc_inverse_mass:
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V_dot_D = numpy.einsum('kmnab, knoab -> kmoab', dataK.Xbar('Ham', 1)[:,:,:,:,None], dataK.D_H[:,:,:,None,:])
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@ -350,8 +406,9 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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triqs SumkDFT object, interpolated
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"""
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n_inequiv_spin_blocks = sum_k.SP + 1 - sum_k.SO
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mpi.report('Initializing optical conductivity...')
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# up and down are equivalent if SP = 0
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n_inequiv_spin_blocks = sum_k.SP + 1 - sum_k.SO
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# ----------------- set-up input from DFT -----------------------
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if code in ('wien2k', 'elk'):
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@ -383,9 +440,27 @@ def init_spectroscopy(sum_k, code='wien2k', w90_params={}):
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calc_inverse_mass = w90_params['calc_inverse_mass'] if 'calc_inverse_mass' in w90_params else False
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assert all(isinstance(name, bool) for name in [calc_velocity, calc_inverse_mass]), f'Parameter {calc_velocity} or {calc_inverse_mass} not bool!'
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# select contributions to be used
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oc_select = w90_params['oc_select'] if 'oc_select' in w90_params else 'both'
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assert oc_select in ['intra', 'inter', 'both'], '"oc_select" needs to be either ["intra", "inter", "both"]'
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# gauge choice options 'h' for Hamiltonian and 'w' for Wannier
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oc_basis = w90_params['oc_basis'] if 'oc_basis' in w90_params else 'h'
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assert oc_basis in ['h', 'w'], '"oc_basis" needs to be either ["h", "w"]'
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# finally, make sure oc_select is 'both' for oc_basis = 'w'
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if oc_basis == 'w' and oc_select != 'both':
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warn(f'"oc_select" must be "both" for "oc_basis" = "w"!')
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oc_select = 'both'
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# further checks for calc_inverse_mass
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if calc_inverse_mass:
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assert oc_basis == 'h', '"calc_inverse_mass" only implemented for "oc_basis" == "h"'
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assert oc_select == 'both', '"oc_select" not implemented for "calc_inverse_mass"'
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# print some information
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mpi.report(f'{"Basis choice [h (Hamiltonian), w (Wannier)]:":<60s} {oc_basis}')
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mpi.report(f'{"Contributions from [intra(-band), inter(-band), both]:":<60s} {oc_select}')
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# recompute sum_k instances on denser grid
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sum_k, _ = recompute_w90_input_on_different_mesh(sum_k, w90_params['seedname'], nk_optics=w90_params['nk_optics'], pathname=pathname,
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calc_velocity=calc_velocity, calc_inverse_mass=calc_inverse_mass)
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calc_velocity=calc_velocity, calc_inverse_mass=calc_inverse_mass, oc_select=oc_select, oc_basis=oc_basis)
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# k-dependent-projections.
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# to be checked. But this should be obsolete atm, works for both cases
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@ -439,6 +514,8 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
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frequency mesh of the optical conductivity recomputed on the mesh provided by the self energy
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"""
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mpi.report('Computing transport distribution...')
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n_inequiv_spin_blocks = sum_k.SP + 1 - sum_k.SO
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# up and down are equivalent if SP = 0
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@ -569,13 +646,12 @@ def transport_distribution(sum_k, beta, directions=['xx'], energy_window=None, O
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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, int(iw + iOm_mesh[iq])]),
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vel_R[v_i, v_i, dir_to_int[direction[1]]]), A_kw[isp][A_i, A_i, iw]).trace().real * sum_k.bz_weights[ik])
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for direction in directions:
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Gamma_w[direction] = (mpi.all_reduce(mpi.world, Gamma_w[direction], lambda x, y: x + y) / sum_k.cell_vol / sum_k.n_symmetries)
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return Gamma_w, omega, temp_Om_mesh
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def transport_function(beta, directions, hopping, velocities, energy_window, n_om):
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def transport_function(beta, directions, hopping, velocities, energy_window, n_om, rot_symmetries):
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r"""
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Calculates the transport function
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@ -600,6 +676,8 @@ def transport_function(beta, directions, hopping, velocities, energy_window, n_o
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n_om : integer
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Number of equidistant frequency points in the interval [energy_window[0]-max(Om_mesh), energy_window[1]+max(Om_mesh)]. This parameters is only used if
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with_Sigma = False.
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rot_symmetries : list of 3 x 3 matrices
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rotational symmetries to restore the full FBZ
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Returns
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-------
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@ -607,6 +685,11 @@ def transport_function(beta, directions, hopping, velocities, energy_window, n_o
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transport function in each direction, frequencies given by energy_window
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"""
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mpi.report('Computing transport function...')
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# check that velocities are computed on the FBZ
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assert numpy.shape(rot_symmetries)[0] == 1, 'Using symmetries currently not implemented for transport function.'
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dir_to_int = {'x': 0, 'y': 1, 'z': 2}
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tol = 1/beta
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@ -619,7 +702,8 @@ def transport_function(beta, directions, hopping, velocities, energy_window, n_o
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fermi_wg = fermi_dis(hopping[:,0,range(orb_1),range(orb_2)][idx].real - w, beta, 1)/fermi_dis(0., beta, 1)
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for direction in directions:
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dir_a, dir_b = [dir_to_int[x] for x in direction]
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transp_func[direction][ct] = numpy.sum(fermi_wg * velocities[:,range(orb_1),range(orb_2),dir_a][idx] * velocities[:,range(orb_1),range(orb_2),dir_b][idx], axis=0).real
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matrix_product = numpy.einsum('kmn, kno -> kmo' , velocities[:,:,:,dir_a], velocities[:,:,:,dir_b])
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transp_func[direction][ct] = numpy.sum(fermi_wg * matrix_product[:,range(orb_1),range(orb_2)][idx]).real
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return transp_func
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@ -727,6 +811,8 @@ def conductivity_and_seebeck(Gamma_w, omega, Om_mesh, SP, directions, beta, meth
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thermal conductivity in each direction. If zero is not present in Om_mesh the thermal conductivity is set to NaN
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"""
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mpi.report('Computing optical conductivity and kinetic coefficients...')
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if not (mpi.is_master_node()):
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return
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