kwant.system.FiniteSystem

class kwant.system.FiniteSystem

Bases: System

Abstract finite low-level system, possibly with leads.

leads

Each lead has to provide a method selfenergy that has the same signature as InfiniteSystem.selfenergy (without the self parameter), and must have property parameters: a collection of strings that name the system parameters ( though this requirement is provisional and may be removed in a future version of Kwant). It may also provide modes that has the same signature as InfiniteSystem.modes (without the self parameter).

Type:

sequence of leads

lead_interfaces

Each sub-sequence contains the indices of the system sites to which the lead is connected.

Type:

sequence of sequences of integers

lead_paddings

Each sub-sequence contains the indices of the system sites that belong to the lead, and therefore have the same onsite as the lead sites, and are connected by the same hoppings as the lead sites.

Type:

sequence of sequences of integers

parameters

The names of the parameters on which the system depends. This does not include the parameters for any leads. This attribute is provisional and may be changed in a future version of Kwant

Type:

frozenset of strings

Notes

The length of leads must be equal to the length of lead_interfaces and lead_paddings.

For lead n, the method leads[n].selfenergy must return a square matrix whose size is sum(len(self.hamiltonian(site, site)) for site in self.lead_interfaces[n]). The output of leads[n].modes has to be a tuple of PropagatingModes, StabilizedModes.

Often, the elements of leads will be instances of InfiniteSystem. If this is the case for lead n, the sites lead_interfaces[n] match the first len(lead_interfaces[n]) sites of the InfiniteSystem.

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’.

abstract 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.

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’.