class TBLattice:
def __init__(self,
units,
hopping,
orbital_positions=[(0, 0, 0)],
orbital_names=[""]):
# the k are int32 which boost python does like to convert
def reg(k):
return tuple(int(x) for x in k)
self._hop = dict((reg(k), np.array(v)) for k, v in hopping.items())
orb = dict((str(i), orb) for (i, orb) in enumerate(orbital_positions))
self.bl = BravaisLattice(units, orbital_positions)
self.bz = BrillouinZone(self.bl)
self.tb = TightBinding(self.bl, self._hop) #, orbital_positions )
self.dim = self.bl.dim
self.NOrbitalsInUnitCell = self.bl.n_orbitals
self.Units = units
self.OrbitalPositions = orbital_positions
self.OrbitalNames = orbital_names
self.MuPattern = np.identity(self.NOrbitalsInUnitCell)
def latt_to_real_x(self, p):
return self.bl.lattice_to_real_coordinates(np.array(p, np.float64))
def hopping_dict(self):
return self._hop
def hopping(self, k_stack):
return hopping_stack(self.tb, k_stack)
def periodization_matrix(self, n_k):
n_k = np.array(n_k)
assert (len(n_k) == 3)
assert (n_k.dtype == np.int)
periodization_matrix = np.diag(np.array(list(n_k), dtype=np.int32))
return periodization_matrix
def get_kmesh(self, n_k):
return MeshBrillouinZone(self.bz, self.periodization_matrix(n_k))
def get_rmesh(self, n_k):
return MeshCyclicLattice(self.bl, self.periodization_matrix(n_k))
def on_mesh_brillouin_zone(self, n_k):
target_shape = [self.NOrbitalsInUnitCell] * 2
kmesh = self.get_kmesh(n_k)
e_k = Gf(mesh=kmesh, target_shape=target_shape)
k_vec = np.array([k.value for k in kmesh])
k_vec_rel = np.dot(np.linalg.inv(self.bz.units()).T, k_vec.T).T
e_k.data[:] = self.hopping(k_vec_rel.T).transpose(2, 0, 1)
return e_k
class TBLattice(object):
""" Class describing a tight binding lattice model.
This class is based in the TRIQS tight binding class and has been extended with
some extra convienience methods and documentation.
Parameters
----------
units : list of three-tuples of floats
Basis vectors for the real space lattice.
hopping : dict
Dictionary with three tuple of integeers as keys,
describing real space hoppings in multiples of
the real space lattice basis vectors, and values being
numpy ndarray hopping matrices in the orbital indices.
orbital_positions : list of three three-tuples of floats.
Internal orbital positions in the unit-cell.
orbital_names : list of strings
Names for each orbital.
"""
def __init__ (self, units, hopping, orbital_positions = [ (0, 0, 0) ], orbital_names = [""]):
# the k are int32 which boost python does like to convert
def reg(k) : return tuple( int(x) for x in k)
self._hop = dict ( ( reg(k), np.array(v)) for k, v in hopping.items())
orb = dict ( (str(i), orb) for (i, orb) in enumerate(orbital_positions ))
self.bl = BravaisLattice(units, orbital_positions)
self.bz = BrillouinZone(self.bl)
self.tb = TightBinding(self.bl, self._hop) #, orbital_positions )
self.dim = self.bl.dim
self.NOrbitalsInUnitCell = self.bl.n_orbitals
self.Units = units
self.OrbitalPositions = orbital_positions
self.OrbitalNames = orbital_names
self.MuPattern = np.identity(self.NOrbitalsInUnitCell)
def latt_to_real_x(self, p) :
return self.bl.lattice_to_real_coordinates (np.array(p, np.float64))
def hopping_dict(self) : return self._hop
def hopping(self, k_stack) :
return hopping_stack(self.tb, k_stack)
def periodization_matrix(self, n_k):
n_k = np.array(n_k)
assert( len(n_k) == 3 )
assert( n_k.dtype == np.int )
periodization_matrix = np.diag(np.array(list(n_k), dtype=np.int32))
return periodization_matrix
def get_kmesh(self, n_k):
return MeshBrillouinZone(self.bz, self.periodization_matrix(n_k))
def get_rmesh(self, n_k):
return MeshCyclicLattice(self.bl, self.periodization_matrix(n_k))
def on_mesh_brillouin_zone(self, n_k):
""" Construct a discretization of the tight binding model in
reciprocal space with given number of k-points.
Parameters
----------
n_k : three-tuple of ints
Number of k-points in every dimension.
Returns
-------
e_k : TRIQS Greens function on a Brillioun zone mesh
Reciprocal space tight binding dispersion.
"""
target_shape = [self.NOrbitalsInUnitCell] * 2
kmesh = self.get_kmesh(n_k)
e_k = Gf(mesh=kmesh, target_shape=target_shape)
k_vec = np.array([k.value for k in kmesh])
k_vec_rel = np.dot(np.linalg.inv(self.bz.units()).T, k_vec.T).T
e_k.data[:] = self.hopping(k_vec_rel.T).transpose(2, 0, 1)
return e_k