lattice_top

A package for lattice-based topological insulator calculations. This repo is mostly bult around a single class - the lattice system class. The class contains a bunch of protocols for creating a quantum system on a lattice, and then calculating various local markers.

Lattice System Class Structure

The class methods can be divided into a few sections.

Initialising the system:

The parent class does not initialise the system - this is left to a few subclasses to allow for a wider variety of quantum systems to be included. Whatever the system we have initialised, the same few internal parameters need to be set:

• _lengths: system size, set by initialisation.
• _edges: boundary conditions, set by initialisation.

Then the initialiser must set a few internal parameters:

• _x_list: list of the x position of every site.
• _y_list: list of the y position of every site.
• _hamiltonian: the hamiltonian for the system.
• _x_dif_hamiltonian: derivative of the hamiltonian with respect to a uniform magnetic vector potential in the x direction - used to calculate the adiabatic bott index and local kubo.
• _y_dif_hamiltonian: derivative of the hamiltonian with respect to a uniform magnetic vector potential in the xy direction - used to calculate the adiabatic bott index and local kubo.
• _n_sites: number of sites in the system

Individual initialisers may also set their own internal parameters, but they shouldnt be used for general calculations - only for methods specific to that individual type of system.

QWZ_System

This initialises a Qi-Wu-Zhang model on a grid. Sets the additional internal parameter:

• _u_vals: gives you the u internal parameter for every site.

Amorphous_System

This sets up an amorphous lattice and builds a hamiltonian on that lattice. The first part is to set up the lattice. The second is to decorate it with a Hamiltonian This sets the additional parameters:

• _sites: list of the coordinates of every site
• _connections: list of pairs of indices of sites that are connected by an edge
• _connection_types: a list of which boundary each connection hops over, eg if it hops over the PBC in the x or y direction