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

Experimental

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

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