import numpy as np
import kwant
from scipy.sparse import coo_array
from itertools import product
import inspect
from copy import copy
def builder2h_0(builder, params={}, return_data=False):
"""
Constructs a tight-binding model dictionary from a `kwant.Builder`.
Parameters:
-----------
builder : `kwant.Builder`
Either builder for non-interacting system or interacting Hamiltonian.
params : dict
Dictionary of parameters to evaluate the Hamiltonian.
return_data : bool
Returns dictionary with sites and number of orbitals per site.
Returns:
--------
h_0 : dict
Tight-binding model of non-interacting systems.
data : dict
Data with sites and number of orbitals. Only if `return_data=True`.
"""
builder = copy(builder)
# Extract information from builder
dims = len(builder.symmetry.periods)
onsite_idx = tuple([0] * dims)
h_0 = {}
sites_list = [*builder.sites()]
norbs_list = [site[0].norbs for site in builder.sites()]
positions_list = [site[0].pos for site in builder.sites()]
norbs_tot = sum(norbs_list)
# Extract onsite and hopping matrices.
# Based on `kwant.wraparound.wraparound`
# Onsite matrices
for site, val in builder.site_value_pairs():
site = builder.symmetry.to_fd(site)
atom = sites_list.index(site)
row = np.sum(norbs_list[:atom]) + range(norbs_list[atom])
col = copy(row)
row, col = np.array([*product(row, col)]).T
try:
for arg in inspect.getfullargspec(val).args:
_params = {}
if arg in params:
_params[arg] = params[arg]
val = val(site, **_params)
data = val.flatten()
except Exception:
data = val.flatten()
if onsite_idx in h_0:
h_0[onsite_idx] += coo_array(
(data, (row, col)), shape=(norbs_tot, norbs_tot)
).toarray()
else:
h_0[onsite_idx] = coo_array(
(data, (row, col)), shape=(norbs_tot, norbs_tot)
).toarray()
# Hopping matrices
for hop, val in builder.hopping_value_pairs():
a, b = hop
b_dom = builder.symmetry.which(b)
b_fd = builder.symmetry.to_fd(b)
atoms = np.array([sites_list.index(a), sites_list.index(b_fd)])
row, col = [
np.sum(norbs_list[: atoms[0]]) + range(norbs_list[atoms[0]]),
np.sum(norbs_list[: atoms[1]]) + range(norbs_list[atoms[1]]),
]
row, col = np.array([*product(row, col)]).T
try:
for arg in inspect.getfullargspec(val).args:
_params = {}
if arg in params:
_params[arg] = params[arg]
val = val(a, b, **_params)
data = val.flatten()
except Exception:
data = val.flatten()
if tuple(b_dom) in h_0:
h_0[tuple(b_dom)] += coo_array(
(data, (row, col)), shape=(norbs_tot, norbs_tot)
).toarray()
if np.linalg.norm(b_dom) == 0:
h_0[tuple(b_dom)] += (
coo_array((data, (row, col)), shape=(norbs_tot, norbs_tot))
.toarray()
.T.conj()
)
else:
# Hopping vector in the opposite direction
h_0[tuple(-b_dom)] += (
coo_array((data, (row, col)), shape=(norbs_tot, norbs_tot))
.toarray()
.T.conj()
)
else:
h_0[tuple(b_dom)] = coo_array(
(data, (row, col)), shape=(norbs_tot, norbs_tot)
).toarray()
if np.linalg.norm(b_dom) == 0:
h_0[tuple(b_dom)] += (
coo_array((data, (row, col)), shape=(norbs_tot, norbs_tot))
.toarray()
.T.conj()
)
else:
h_0[tuple(-b_dom)] = (
coo_array((data, (row, col)), shape=(norbs_tot, norbs_tot))
.toarray()
.T.conj()
)
if return_data:
data = {}
data["norbs"] = norbs_list
data["positions"] = positions_list
return h_0, data
else:
return h_0
def build_interacting_syst(builder, lattice, func_onsite, func_hop, max_neighbor=1):
"""
Construct an auxiliary `kwant` system to build Hamiltonian matrix.
Parameters:
-----------
builder : `kwant.Builder`
Non-interacting `kwant` system.
lattice : `kwant.lattice`
System lattice.
func_onsite : function
Onsite function.
func_hop : function
Hopping function.
max_neighbor : int
Maximal nearest-neighbor order.
Returns:
--------
int_builder : `kwant.Builder`
Dummy `kwant.Builder` to compute interaction matrix.
"""
int_builder = kwant.Builder(kwant.TranslationalSymmetry(*builder.symmetry.periods))
int_builder[builder.sites()] = func_onsite
for neighbors in range(max_neighbor):
int_builder[lattice.neighbors(neighbors + 1)] = func_hop
return int_builder
def generate_guess(vectors, ndof, scale=1):
"""
vectors : list
List of hopping vectors.
ndof : int
Number internal degrees of freedom (orbitals),
scale : float
The scale of the guess. Maximum absolute value of each element of the guess.
Returns:
--------
guess : tb dictionary
Guess in the form of a tight-binding model.
"""
guess = {}
for vector in vectors:
if vector not in guess.keys():
amplitude = scale * np.random.rand(ndof, ndof)
phase = 2 * np.pi * np.random.rand(ndof, ndof)
rand_hermitian = amplitude * np.exp(1j * phase)
if np.linalg.norm(np.array(vector)) == 0:
rand_hermitian += rand_hermitian.T.conj()
rand_hermitian /= 2
guess[vector] = rand_hermitian
else:
guess[vector] = rand_hermitian
guess[tuple(-np.array(vector))] = rand_hermitian.T.conj()
return guess
def generate_vectors(cutoff, dim):
"""
Generates hopping vectors up to a cutoff.
Parameters:
-----------
cutoff : int
Maximum distance along each direction.
dim : int
Dimension of the vectors.
Returns:
--------
List of hopping vectors.
"""
return [*product(*([[*range(-cutoff, cutoff + 1)]] * dim))]
def calc_gap(vals, E_F):
"""
Compute gap.
Parameters:
-----------
vals : nd-array
Eigenvalues on a k-point grid.
E_F : float
Fermi energy.
Returns:
--------
gap : float
Indirect gap.
"""
emax = np.max(vals[vals <= E_F])
emin = np.min(vals[vals > E_F])
return np.abs(emin - emax)