kwant.builder.InfiniteSystem

class kwant.builder.InfiniteSystem(builder, interface_order=None)

Bases: _FinalizedBuilderMixin, InfiniteSystem

Finalized infinite system, extracted from a Builder.

sites

sites[i] is the Site instance that corresponds to the integer-labeled site i of the low-level system.

Type:

sequence

id_by_site

The inverse of sites; maps high-level Site instances to their integer label. Satisfies id_by_site[sites[i]] == i.

Type:

dict

Notes

In infinite systems sites consists of 3 parts: sites in the fundamental domain (FD) with hoppings to neighboring cells, sites in the FD with no hoppings to neighboring cells, and sites in FD+1 attached to the FD by hoppings. Each of these three subsequences is individually sorted.

Finalize a builder instance which has to have exactly a single symmetry direction.

If interface_order is not set, the order of the interface sites in the finalized system will be arbitrary. If interface_order is set to a sequence of interface sites, this order will be kept.

Methods

cell_hamiltonian(args=(), sparse=False, *, params=None)

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)

Return the discrete symmetry of the system.

The returned object is an instance of DiscreteSymmetry.

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

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.

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

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.

inter_cell_hopping(args=(), sparse=False, *, params=None)

Hopping Hamiltonian between two cells of the infinite system.

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

modes(energy=0, args=(), *, params=None)

Return mode decomposition of the lead

This is a wrapper around kwant.physics.modes. The said function is applied to the infinite system at hand. Any discrete symmetries that are declared for the system are validated, and, if present, passed on as well. (Warnings are emitted for declared symmetries that are broken.)

The result of the wrapped function (an instance of PropagatingModes along with an instance of StabilizedModes) is returned unchanged.

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’.

pos(i)

selfenergy(energy=0, args=(), *, params=None)

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)

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’.