# API Reference¶

This detailed reference lists all the classes and functions contained in the package. If you are just looking to get started, read the Tutorial first.

The Lattice describes the unit cell of a crystal, while the Model is used to build up a larger system by translating the unit cell to fill a certain shape or symmetry. The model builds the Hamiltonian matrix by applying fields and other modifier parameters.

 Lattice(a1[, a2, a3]) Unit cell of a Bravais lattice, the basic building block of a tight-binding model Model(lattice, *args) Builds a Hamiltonian from lattice, shape, symmetry and modifier parameters

## Shapes¶

The geometry of a finite-sized system can be defined using the Polygon class (2D only) or using FreeformShape (1 to 3 dimensions). A few common shapes are included in the package and listed below. These predefined shapes are just functions which configure and return a shape class object.

Building blocks

 Polygon(vertices) Shape defined by a list of vertices in a 2D plane FreeformShape(contains, width[, center]) Shape in 1 to 3 dimensions, defined by a function and a bounding box CompositeShape(shape1, shape2, op) A composition of 2 shapes using some operator (and, or, xor…)

Predefined shapes

 circle(radius[, center]) A circle in the xy plane line(a, b) A line shape intended for 1D lattices or to specify leads for 2D lattices primitive([a1, a2, a3]) Follow the primitive lattice shape – just repeat the unit cell a number of times rectangle(x[, y]) A rectangle in the xy plane regular_polygon(num_sides, radius[, angle]) A polygon shape where all sides have equal length

## Symmetry¶

 translational_symmetry([a1, a2, a3]) Simple translational symmetry

## Modifiers¶

The following decorators are used to create functions which express some feature of a tight-binding model, such as various fields, defects or geometric deformations.

Decorators

 site_state_modifier([min_neighbors]) Modify the state (valid or invalid) of lattice sites, e.g. to create vacancies site_position_modifier() Modify the position of lattice sites, e.g. to apply geometric deformations onsite_energy_modifier([is_double]) Modify the onsite energy, e.g. to apply an electric field hopping_energy_modifier([is_double, is_complex]) Modify the hopping energy, e.g. to apply a magnetic field

Predefined modifiers

 constant_potential(magnitude) Apply a constant onsite energy to every lattice site force_double_precision() Forces the model to use double precision even if that’s not require by any modifier force_complex_numbers() Forces the model to use complex numbers even if that’s not require by any modifier

## Generators¶

The following decorators are used to create functions which add features to a tight-binding model, such as hoppings and sites.

Decorators

 hopping_generator(name, energy) Introduce a new hopping family (with a new hop_id) via a list of index pairs site_generator(name, energy) Introduce a new site family (with a new sub_id) via a list of site positions

## Compute¶

After a Model is constructed, computational routines can be applied to determine various physical properties. The following submodules contain functions for exact diagonalization as well as some approximative compute methods. Follow the links below for details.

 solver Eigensolvers with a few extra computation methods chebyshev Computations based on Chebyshev polynomial expansion

Experimental

 parallel Multi-threaded functions for parameter sweeps

## Results¶

Result objects are usually produced by compute functions, but they are also used to express certain model properties. They hold data and offer postprocessing and plotting methods specifically adapted to the nature of the physical properties (i.e. the stored data).

The utility functions pb.save() and pb.load() can be used to efficiently store entire result objects into files. The information about the kind of physical property is saved along with the raw data, i.e. executing result = pb.load("data_file.pbz") followed by result.plot() will work and present the appropriate figure.

 save(obj, file) Save an object to a compressed file load(file) Load an object from a compressed file make_path(k0, k1, *ks[, step]) Create a path which connects the given k points Bands(k_path, energy) Band structure along a path in k-space Eigenvalues(eigenvalues[, probability]) Hamiltonian eigenvalues with optional probability map Series(variable, data[, labels]) A series of data points determined by a common relation, i.e. SpatialMap(data, positions[, sublattices]) Represents some spatially dependent property: data mapped to site positions StructureMap(data, sites, hoppings[, boundaries]) A subclass of SpatialMap that also includes hoppings between sites Sweep(x, y, data[, labels, tags]) 2D parameter sweep with x and y 1D array parameters and data 2D array result NDSweep(variables, data[, labels, tags]) ND parameter sweep

## Components¶

The following submodules contain classes and functions which are not meant to created manually, but they are components of other classes (e.g. Model) so they are used regularly (even if indirectly).

 system Structural information and utilities leads Lead interface for scattering models

## Miscellaneous¶

 constants A few useful physical constants pltutils Collection of utility functions for matplotlib