The Mathematica package HyperBloch

HyperBloch is a Mathematica package for constructing tight-binding models on hyperbolic lattices and calculating their band structures using the supercell method. The package needs as input a crystallographic information for the corresponding hyperbolic lattice, which can be generated using the related GAP package HyperCells.

The package can be downloaded from Github, and a detailed documentation is imported into the Mathematica environment upon installing the paclet file. 

The package is based on

• P. M. Lenggenhager, J. Maciejko, and T. Bzdušek, Non-Abelian hyperbolic band theory from supercells, Phys. Rev. Lett. 131, 226401 (2023) (publicly accessible preprint atarXiv:2305.04945).

and the doctoral thesis

• P. M. Lenggenhager, Emerging avenues in band theory: multigap topology and hyperbolic lattices, PhD thesis, ETH Zurich (2023)

Basic functionality is demonstrated in the Supplmentary Code and Data associated with the PRL manuscript. In addition, we are planning to upload tutorials that showcase the implementation of several standard constructions by June 2024.

If you use this package, please cite at least one of the above references in addition to the package itself:

• P. M. Lenggenhager, J. Maciejko, and T. Bzdušek, HyperBloch: A Mathematica package for hyperbolic tight-binding models and the supercell method, https://github.com/patrick-lenggenhager/HyperBloch (2023)