triqs.lattice.tight_binding.TBLattice

class triqs.lattice.tight_binding.TBLattice(units, hoppings={}, orbital_positions=[(0, 0, 0)], orbital_names=None, hopping=None)[source]

Bases: object

A tight-binding Hamiltonian on top of a Bravais lattice.

Bundles a BravaisLattice, a BrillouinZone and a TightBinding instance and exposes part of their interfaces directly.

Parameters:

unitslist of tuples of floats: Basis vectors of the real-space lattice.
hoppingsdict, optional: Dictionary mapping tuples of integers (real-space displacements in multiples of the lattice basis vectors) to numpy ndarray hopping matrices over the orbital indices.
orbital_positionslist of three-tuples of floats, optional: Internal orbital positions in the unit cell.
orbital_nameslist of str, optional: Names for each orbital.

Attributes

`hoppings`	Real-space hoppings as a `{displacement: matrix}` dict.
`ndim`	Number of spatial dimensions of the lattice.
`units`	Lattice basis vectors as a `(ndim, ndim)` array in the standard basis.
`n_orbitals`	Number of orbitals in the unit cell.
`orbital_positions`	Positions of the orbitals inside the unit cell.
`orbital_names`	Names of the orbitals in the unit cell.

bl	(BravaisLattice) The associated Bravais lattice.
bz	(BrillouinZone) The associated Brillouin zone.
tb	(TightBinding) The tight-binding Hamiltonian.

Methods

`dispersion`(arg)	Compute the dispersion, i.e. the eigenvalue spectrum of \(h_{\mathbf{k}}\), for a given momentum vector.
`fourier`(arg)	Compute the Fourier transform for a given momentum vector (or array of momentum vectors).
`get_kmesh`(n_k)	Return a mesh on the Brillouin zone with a given discretization.
`get_rmesh`(n_r)	Return a mesh on the Bravais lattice with a given periodicity.
`lattice_to_real_coordinates`(x)	Transform a vector from the lattice basis to the standard basis.

Examples

A nearest-neighbour tight-binding model on the 2D square lattice:

>>> from triqs.lattice.tight_binding import TBLattice, dos
>>> t = 1.0
>>> TB = TBLattice(
...     units=[(1, 0, 0), (0, 1, 0)],
...     hoppings={( 1, 0): [[-t]], (-1,  0): [[-t]],
...               ( 0, 1): [[-t]], ( 0, -1): [[-t]]},
...     orbital_positions=[(0, 0, 0)])

Compute its density of states on a regular k-grid (one DOS per band):

>>> d = dos(TB, n_kpts=100, n_eps=100, name='square')[0]

Build a k-mesh on the Brillouin zone for further calculations:

>>> kmesh = TB.get_kmesh(n_k=32)