kwant.builder.FiniteSystem

class kwant.builder.FiniteSystem(builder)

Bases: _FinalizedBuilderMixin, FiniteSystem

Finalized Builder with leads.

Usable as input for the solvers in kwant.solvers.

sites

sites[i] is the Site instance that corresponds to the integer-labeled site i of the low-level system. The sites are ordered first by their family and then by their tag.

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

Methods

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.

pos(i)

precalculate(energy=0, args=(), leads=None, what='modes', *, params=None)

Precalculate modes or self-energies in the leads.

Construct a copy of the system, with the lead modes precalculated, which may significantly speed up calculations where only the system is changing.

Parameters:

• energy (float) – Energy at which the modes or self-energies have to be evaluated.

• args (sequence) – Additional parameters required for calculating the Hamiltionians. Deprecated in favor of ‘params’ (and mutually exclusive with it).

• leads (sequence of integers or None) – Numbers of the leads to be precalculated. If None, all are precalculated.

• what ('modes', 'selfenergy', 'all') – The quantitity to precompute. ‘all’ will compute both modes and self-energies. Defaults to ‘modes’.

• params (dict, optional) – Dictionary of parameter names and their values. Mutually exclusive with ‘args’.

Returns:

syst – A copy of the original system with some leads precalculated.

Return type:

FiniteSystem

Notes

If the leads are precalculated at certain energy or args values, they might give wrong results if used to solve the system with different parameter values. Use this function with caution.

validate_symmetries(args=(), *, params=None)

Check that the Hamiltonian satisfies discrete symmetries.

Applies validate to the Hamiltonian, 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’.