kwant.continuum.discretize(hamiltonian, coords=None, *, grid=None, locals=None, grid_spacing=None)[source]

Construct a tight-binding model from a continuum Hamiltonian.

If necessary, the given Hamiltonian is sympified using kwant.continuum.sympify. It is then discretized symbolically and turned into a Builder instance that may be used with fill.

This is a convenience function that is equivalent to first calling discretize_symbolic and feeding its result into build_discretized.


This function uses eval (because it calls sympy.sympify), and thus should not be used on unsanitized input.

hamiltonianstr or SymPy expression

Symbolic representation of a continuous Hamiltonian. It is converted to a SymPy expression using kwant.continuum.sympify.

coordssequence of strings, optional

The coordinates for which momentum operators will be treated as differential operators. May contain only “x”, “y” and “z” and must be sorted. If not provided, coords will be obtained from the input Hamiltonian by reading the present coordinates and momentum operators.

gridscalar or kwant.lattice.Monatomic instance, optional

Lattice that will be used as a discretization grid. It must have orthogonal primitive vectors. If a scalar value is given, a lattice with the appropriate grid spacing will be generated. If not provided, a lattice with grid spacing 1 in all directions will be generated.

localsdict, optional

Additional namespace entries for sympify. May be used to simplify input of matrices or modify input before proceeding further. For example: locals={'k': 'k_x + I * k_y'} or locals={'sigma_plus': [[0, 2], [0, 0]]}.

grid_spacingint or float, optional

(deprecated) Spacing of the discretization grid. If unset the default value will be 1. Cannot be used together with grid.


The translationally symmetric builder that corresponds to the provided Hamiltonian. This builder instance belongs to a subclass of the standard builder that may be printed to obtain the source code of the value functions. It also holds the discretization lattice (a Monatomic instance with lattice constant grid_spacing) in the lattice attribute.

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4.4. kwant.continuum – Tools for continuum systems

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