Source code for triqs.lattice.utils

# Copyright (c) 2021 Simons Foundation
# This program 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.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# GNU General Public License for more details.
# You may obtain a copy of the License at
# Authors: Nils Wentzell

from io import StringIO
import numpy as np

__all__ = ['k_space_path', 'TB_from_wannier90']

[docs]def k_space_path(paths, num=101, bz=None): """ Generate an array of k-vectors along a path defined by a list of pairs of k-vectors Parameters ---------- paths : list of pairs of three-vectors of floats List of pairs of k-vectors (in reciprocal units) to create a path in-between. num : int, default=100 Number of k-vectors along each segment the paths bz : brillouin_zone, optional When a Brillouin Zone is passed, calculate distance in absolute units Returns ------- kvecs: numpy.array [shape=(len(paths)*num,3)] Two-dimensional numpy array containing the path vectors (in reciprocal units) as rows dist: numpy.array [shape=(kvecs.shape[0])] One-dimensional numpy array containing, for each element in kvecs, the distance travelled along the path. Useful for plotting. If bz is provided, calculate the distance in absolute units. The distances for the relevant k-points in paths can be obtained with dist[num-1::num]. """ if bz is None: cell = np.eye(3) else: cell = bz.units x = np.linspace(0., 1., num=num) kvecs = [ki[None, :] + x[:, None] * (kf - ki)[None, :] for ki, kf in paths] cur_dist = 0.0 dist = np.array([], dtype=float) for kvec in kvecs: kvec_abs =, cell) dist_new = np.linalg.norm(kvec_abs - kvec_abs[0], axis=1) + cur_dist dist = np.concatenate((dist, dist_new)) cur_dist = dist[-1] return np.vstack(kvecs), dist
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[docs]def parse_hopping_from_wannier90_hr_dat(filename): r""" Wannier90 real space hopping parser of ``*_hr.dat`` files. Returns a dictionary where the keys are the real-space hopping vectors, in terms of multiples of the lattice vectors, and the values are ``num_wann * num_wann`` numpy ndarrays with the hopping integrals. Parameters ---------- filename : str Wannier90 ``*_hr.dat`` file to parse. Returns ------- hopp_dict : dict Dictionary of real space hoppings. num_wann : int Total number of Wannier functions per unit-cell. """ with open(filename, 'r') as fd: fd.readline() # eliminate time header num_wann = int(fd.readline()) nrpts = int(fd.readline()) lines = fd.readlines() # Read R Vector degeneracies, At most 15 elements before line-break nlines = int(np.ceil(nrpts / 15.)) deg = np.array("".join(lines[:nlines]).split(), dtype=int) assert deg.shape == (nrpts,) # Read R Vector and Hopping data dat = "".join(lines[nlines:]) dat = np.loadtxt(StringIO(dat)) dat = dat.reshape(nrpts, num_wann, num_wann, 7) R = dat[:, 0, 0, 0:3].astype(int) hopp = dat[..., 5] + 1.j * dat[..., 6] # Account for degeneracy of the Wigner-Seitz points hopp /= deg[:, None, None] # Dict with hopping matrices hopp_dict = {tuple(R[i]): hopp[i] for i in range(nrpts)} return hopp_dict, num_wann
[docs]def parse_lattice_vectors_from_wannier90_wout(filename): r""" Wannier90 real space lattice vectors parser of ``*.wout`` files. Parameters ---------- filename : str Wannier90 ``*.wout`` file to parse. Returns ------- vectors : list of three three-tuples of floats Lattice vectors. """ with open(filename, 'r') as fd: lines = fd.readlines() # -- Find start of data in text file for idx, line in enumerate(lines): if 'Lattice Vectors' in line: if '(Ang)' in line: unit = 1.0 elif '(Bohr)' in line: unit = 0.5291772105638411 else: raise NotImplementedError break if 'Lattice Vectors' not in line: raise IOError # Read vector data and scale by unit length lines = "".join(lines[idx+1:idx+4]) dat = np.loadtxt(StringIO(lines), usecols=(1, 2, 3)) dat *= unit # Convert 3x3 data to list of tuples vectors = [tuple(dat[i]) for i in range(3)] return vectors
[docs]def extend_wannier90_to_spin(hopp_dict, num_wann): hopp_dict_spin = {k: np.kron(np.eye(2), v) for k, v in hopp_dict.items()} return hopp_dict_spin, 2 * num_wann
[docs]def TB_from_wannier90(seed, path='./', extend_to_spin=False, add_local=None): r""" read wannier90 output and convert to TBLattice object reads wannier90 real space lattice vectors from seed.wout file. reads wannier90 hoppings from seed_hr.dat file Parameters ---------- seed : str seedname of wannier90 run, name of *_hr.dat path : str, default = './' path to wannier90 output dir extend_to_spin: bool, default= False extend hopping Hamiltonian with spin indices add_local: numpy array , default = None add a local term to hopping[0,0,0] of shape Norb x Norb Returns ------- TBL : triqs TBLattice object triqs tight binding object """ from triqs.lattice.tight_binding import TBLattice hopp_dict, num_wann = parse_hopping_from_wannier90_hr_dat(path + seed + '_hr.dat') units = parse_lattice_vectors_from_wannier90_wout(path + seed + '.wout') if extend_to_spin: hopp_dict, num_wann = extend_wannier90_to_spin(hopp_dict, num_wann) if add_local is not None: hopp_dict[(0, 0, 0)] += add_local # Should we use hopp_dict or hopping? TBL = TBLattice(units=units, hoppings=hopp_dict, orbital_positions=[(0, 0, 0)]*num_wann, orbital_names=[str(i) for i in range(num_wann)]) return TBL
[docs]def TB_from_pythTB(ptb): r""" convert pythTB model to TBLattice object Parameters ---------- ptb : pythtb.tb_model pythTB tight-binding object Returns ------- TBL : triqs TBLattice object triqs tight binding object """ from triqs.lattice.tight_binding import TBLattice # initialize objects hopp_dict = {} m_zero = np.zeros((ptb.get_num_orbitals(), ptb.get_num_orbitals()), dtype=complex) # fill on-site energies hopp_dict[(0, 0, 0)] = np.eye(ptb.get_num_orbitals(), dtype=complex) * ptb._site_energies # fill hoppings for hopp, orb_from, orb_to, displacement in ptb._hoppings: if tuple(displacement) not in hopp_dict: hopp_dict[tuple(displacement)] = m_zero.copy() # per default pythTB does not explicitly stores -R hopp_dict[tuple(-np.array(displacement))] = m_zero.copy() hopp_dict[tuple(displacement)][orb_from, orb_to] += hopp # fill -R from +R using H_ij(+R)=[H_ji(-R)]* # if the user specified -R explicitly we have to sum both hopping matrices # according to pythTB documentation hopp_dict[tuple(-np.array(displacement))][orb_to, orb_from] += np.conj(hopp) TBL = TBLattice(units=ptb.get_lat(), hopping=hopp_dict, orbital_positions=ptb.get_orb(), orbital_names=[str(i) for i in range(ptb.get_num_orbitals())]) return TBL