HyperBloch

HyperBloch is a Mathematica package for constructing tight-binding models on hyperbolic lattices and calculating their band structures using the supercell method.

:book: We have a new website with detailed instructions on the installation process, a getting-started guide and hands-on tutorials: https://www.hypercells.net.

An introduction to the underlying concepts can be found in the following publication

P. M. Lenggenhager, J. Maciejko, and T. Bzdušek, Non-Abelian hyperbolic band theory from supercells, Phys. Rev. Lett. 131, 226401 (2023)

and the doctoral thesis

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

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/HyperCells/HyperBloch, 10.5281/zenodo.10222865 (2023)

This post in the Wolfram Community forum demonstrates some of the core functionality of the package.

Please refer to CONTRIBUTING.md on how you can contribute to the development of this package.

#### Table of Contents
- HyperBloch - Table of Contents - Authors and developers - Installation - Dependencies - HyperBloch - Documentation - Limitations - HyperCells package - How to cite - Contact - License and copyright

Authors and developers

Main developer:\   Patrick M. Lenggenhager\   Email: plengg@pks.mpg.de\   Website: https://patrick-lenggenhager.github.io

Coauthors:\   Joseph Maciejko (maciejko@ualberta.ca)\   Tomáš Bzdušek (tomas.bzdusek@uzh.ch)

Code contributers:\   Marcelo Looser (marcelo.looser@outlook.com)

Installation

Dependencies

HyperBloch requires the NCAlgebra package, which is available from GitHub at https://github.com/NCAlgebra/NC Please check the installation instructions there.

HyperBloch

In the future, HyperBloch will be submitted to the Wolfram Language Paclet Repository. Until then, it can be installed manually. For version 1.0.1, the following command can be used: Mathematica PacletInstall["https://github.com/HyperCells/HyperBloch/releases/download/v1.0.1/PatrickMLenggenhager__HyperBloch-1.0.1.paclet"]

Alternatively, you can download the latest release (as a .paclet file) from https://github.com/HyperCells/HyperBloch/releases/latest, open Mathematica and evaluate Mathematica PacletInstall["path/to/PatrickMLenggenhager__HyperBloch-x.x.x.paclet"] where path/to/PatrickMLenggenhager__HyperBloch-x.x.x.paclet is the path to the downloaded .paclet file.

Then, load the package by evaluating Mathematica << PatrickMLenggenhager`HyperBloch`

Note that while most of the functionality of HyperBloch is available with Wolfram Language 12.0, some of the visualization functions require Wolfram Language 13 or later, such that updating to Wolfram Language 13 is recommended.

Documentation

The documentation is distributed as part of the paclet and integrates into the Wolfram Language documentation center. To access it, open Mathematica and press F1 or click on the Help menu and select Wolfram Documentation. Then, search for "HyperBloch" in the search bar. A good place to start is the Tech Note "Basic Usage", which is usually among the first few results. Alternatively, you can access the documentation pages directly: PatrickMLenggenhager/HyperBloch/tutorial/BasicUsage.

The Guide page (PatrickMLenggenhager/HyperBloch/guide/HyperBlochPackage) contains an overview over the package and its functionality. The reference pages contain detailed information about the package's functions and options.

Limitations

Note that at this point HyperBloch is still under development and, because the limitations have not yet been fully determined, released only as a beta version. Further testing will be required before an official release. However, the package is already fully functional and documented and can be used to reproduce the results of the publication mentioned above.

In newer versions of Mathematica, the visualization functions may lead to warnings about badly conditioned warnings. These warnings can, in most cases, be safely ignored. For very large cells, the visualization of objects close to the boundary of the Poincaré disk may be inaccurate. However, the deviations will most likely not be visible. If you do encounter visible inaccuracies, please report them using the issue tracker at

https://github.com/HyperCells/HyperBloch/issues

HyperCells package

The HyperCells GAP package is a companion package to HyperBloch. The input HyperBloch requires, i.e., the graphs representing primitive and supercells of hyperbolic lattices and models defined on them, can be generated using HyperCells. It is available on Github at

https://github.com/HyperCells/HyperCells

How to cite

If you use this package, please cite the package repository BibTeX @misc{HyperBloch, title = {{HyperBloch}: {A} {M}athematica package for hyperbolic tight-binding models and the supercell method}, author = {Lenggenhager, Patrick M. and Maciejko, Joseph and Bzdu\v{s}ek, Tom\'{a}\v{s}}, year = {2023}, doi = {10.5281/zenodo.10222865}, note = {\url{https://github.com/HyperCells/HyperBloch}} } and at least one of the following references: ```BibTeX @article{Lenggenhager:2023, title = {Non-{A}belian hyperbolic band theory from supercells}, author = {Lenggenhager, Patrick M. and Maciejko, Joseph and Bzdu\v{s}ek, Tom\'{a}\v{s}}, journal = {Phys. Rev. Lett.}, volume = {131}, issue = {22}, pages = {226401}, numpages = {7}, year = {2023}, month = {Dec}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.131.226401} }

@phdthesis{Lenggenhager:PhDThesis, title = {Emerging avenues in band theory: multigap topology and hyperbolic lattices}, author = {Lenggenhager, Patrick M.}, year = {2023}, school = {ETH Zurich}, doi = {10.3929/ethz-b-000645370} } ```

Contact

To report issues, please use the issue tracker at https://github.com/HyperCells/HyperBloch/issues.

Maintainer:\   Patrick M. Lenggenhager\   Email: plengg@pks.mpg.de\   Homepage: https://patrick-lenggenhager.github.io

License and copyright

HyperBloch is free software; you can redistribute and/or modify it under the terms of the CC BY-SA 4.0 license as described below. HyperBloch is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY, see the CC BY-SA 4.0 license for more details.

This is a human-readable summary of (and not a substitute for) the license, see the attached LICENSE for the full legal text.

You are free to: Share — copy and redistribute the material in any medium or format for any purpose. Adapt — remix, transform, and build upon the material for any purpose. The licensor cannot revoke these freedoms as long as you follow the license terms.

Under the following terms: Attribution - You must give appropriate credit (see AUTHORS and How to cite above), provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. ShareAlike - If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. No additional restrictions - You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

© 2023-2024 Patrick M. Lenggenhager