kwant.system.InfiniteVectorizedSystem

class kwant.system.InfiniteVectorizedSystem[source]

Bases: kwant.system.VectorizedSystem, kwant.system.InfiniteSystemMixin

Abstract vectorized infinite low-level system.

An infinite system consists of an infinite series of identical cells. Adjacent cells are connected by identical inter-cell hoppings.

Notes

Unlike InfiniteSystem, vectorized infinite systems do not explicitly store the sites in the previous unit cell; only the sites in the fundamental domain are stored. Nevertheless, the SiteArrays of InfiniteVectorizedSystem are ordered in an analogous way, in order to facilitate the representation of inter-cell hoppings. The ordering is as follows. The interface sites of a unit cell are the sites that have hoppings to the next unit cell (along the symmetry direction). Interface sites are always in different SiteArrays than non-interface sites, i.e. the sites in a given SiteArray are either all interface sites, or all non-interface sites. The SiteArrays consisting of interface sites always appear before the SiteArrays consisting of non-interface sites in self.site_arrays. This is backwards compatible with kwant.system.InfiniteSystem.

For backwards compatibility, InfiniteVectorizedSystem maintains a graph, that includes nodes for the sites in the previous unit cell.

Attributes
cell_sizeinteger

The number of sites in a single cell of the system.

Methods

cell_hamiltonian(args=(), sparse=False, *, params=None)[source]

Hamiltonian of a single cell of the infinite system.

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

discrete_symmetry(args, *, params=None)[source]

Return the discrete symmetry of the system.

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

abstract hamiltonian(i, j, *args, params=None)[source]

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.

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

hamiltonian_submatrix(args=(), sparse=False, return_norb=False, *, params=None)[source]

Return The system Hamiltonian.

Parameters
argstuple, defaults to empty

Positional arguments to pass to hamiltonian_term. Mutually exclusive with ‘params’.

sparsebool

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

return_norbbool

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

paramsdict, optional

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

Returns
hamiltonian_partnumpy.ndarray or scipy.sparse.coo_matrix

The Hamiltonian of the system.

norbarray of integers

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

Notes

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

abstract hamiltonian_term(index, selector=slice(None, None, None), args=(), params=None)[source]

Return the Hamiltonians for hamiltonian term number k.

Parameters
indexint

The index of the term to evaluate.

selectorslice or sequence of int, default: slice(None)

The elements of the term to evaluate.

argstuple

Positional arguments to the term. (Deprecated)

paramsdict

Keyword parameters to the term

Returns
hamiltonian3d complex array

Has shape (N, P, Q) where N is the number of matrix elements in this term (or the number selected by ‘selector’ if provided), P and Q are the number of orbitals in the ‘to’ and ‘from’ site arrays associated with this term.

Providing positional arguments via ‘args’ is deprecated,
instead, provide named parameters as a dictionary via ‘params’.
inter_cell_hopping(args=(), sparse=False, *, params=None)[source]

Hopping Hamiltonian between two cells of the infinite system.

This method returns a complex matrix that represents the hopping from the interface sites of unit cell n - 1 to all the sites of unit cell n. It is therefore generally a rectangular matrix of shape (N_uc, N_iface) where N_uc is the number of orbitals in the unit cell, and N_iface is the number of orbitals on the interface sites (i.e. the sites with hoppings to the next unit cell).

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

modes(energy=0, args=(), *, params=None)[source]

Return mode decomposition of the lead

See documentation of PropagatingModes and StabilizedModes for the return format details.

The wave functions of the returned modes are defined over the unit cell of the system, which corresponds to the degrees of freedom on the first cell_sites sites of the system (recall that infinite systems store first the sites in the unit cell, then connected sites in the neighboring unit cell).

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

selfenergy(energy=0, args=(), *, params=None)[source]

Return self-energy of a lead.

The returned matrix has the shape (s, s), where s is sum(len(self.hamiltonian(i, i)) for i in range(self.graph.num_nodes - self.cell_size)).

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

validate_symmetries(args=(), *, params=None)[source]

Check that the Hamiltonian satisfies discrete symmetries.

Returns validate applied to the onsite matrix and the hopping. See its documentation for details on the return format.

Providing positional arguments via ‘args’ is deprecated, instead, provide named parameters as a dictionary via ‘params’.

Attributes

site_ranges[source]

Previous topic

kwant.system.InfiniteSystem

Next topic

kwant.system.FiniteSystem

This Page