kwant.system.System

class kwant.system.System

Bases: object

Abstract general low-level system.

Notes

The sites of the system are indexed by integers ranging from 0 to self.graph.num_nodes - 1.

Optionally, a class derived from System can provide a method pos which is assumed to return the real-space position of a site given its index.

Due to the ordering semantics of sequences, and the fact that a given first_site can only appear at most once in site_ranges, site_ranges is ordered according to first_site.

Consecutive elements in site_ranges are not required to have different numbers of orbitals.

Attributes

graph

(kwant.graph.CGraph) The system graph.

site_ranges

(None or sorted sequence of triples of integers) If provided, encodes ranges of sites that have the same number of orbitals. Each triple consists of (first_site, norbs, orb_offset): the first site in the range, the number of orbitals on each site in the range, and the offset of the first orbital of the first site in the range. In addition, the final triple should have the form (len(graph.num_nodes), 0, tot_norbs) where tot_norbs is the total number of orbitals in the system.

Methods

discrete_symmetry(args, *, params=None)

Return the discrete symmetry of the system.

hamiltonian(i, j, *args, params=None)

Return the hamiltonian matrix element for sites i and j.

If i == j, return the on-site Hamiltonian of site i.

if i != j, return the hopping between site i and j.

Hamiltonians may depend (optionally) on positional and keyword arguments

hamiltonian_submatrix(self, args=(), to_sites=None, from_sites=None, sparse=False, return_norb=False, *, params=None)

Return a submatrix of the system Hamiltonian.

Parameters:

args : tuple, defaults to empty

Positional arguments to pass to the hamiltonian method. Mutually exclusive with ‘params’.

to_sites : sequence of sites or None (default)

from_sites : sequence of sites or None (default)

sparse : bool

Whether to return a sparse or a dense matrix. Defaults to False.

return_norb : bool

Whether to return arrays of numbers of orbitals. Defaults to False.

params : dict, optional

Dictionary of parameter names and their values. Mutually exclusive with ‘args’.

Returns:

hamiltonian_part : numpy.ndarray or scipy.sparse.coo_matrix

Submatrix of Hamiltonian of the system.

to_norb : array of integers

Numbers of orbitals on each site in to_sites. Only returned when return_norb is true.

from_norb : array of integers

Numbers of orbitals on each site in from_sites. Only returned when return_norb is true.

Notes

The returned submatrix contains all the Hamiltonian matrix elements from from_sites to to_sites. The default for from_sites and to_sites is None which means to use all sites of the system in the order in which they appear.