HyperCells

A GAP package for constructing primitive cells and supercells of hyperbolic lattices

Version 0.9.0-beta
Released 2023-11-29

This project is maintained by Patrick M. Lenggenhager

GAP Package HyperCells

The current version of this package is version 0.9.0-beta, released on 2023-11-29. For more information, please refer to the package manual. There is also a README file.

Dependencies

This package requires GAP version >= 4.11

Limitations

Note that at this point HyperCells 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.

Known limitations

Authors

Patrick M. Lenggenhager, Joseph Maciejko, Tomáš Bzdušek.

How to cite

If you use this package, please cite the package repository

P. M. Lenggenhager, J. Maciejko, and T. Bzdušek, HyperCells: A GAP package for constructing primitive cells and supercells of hyperbolic lattices, https://github.com/patrick-lenggenhager/HyperCells (2023)

@misc{HyperCells,
  title           = {{H}yper{C}ells: {A} {GAP} package for constructing primitive cells and supercells of hyperbolic lattices},
  author          = {Lenggenhager, Patrick M. and Maciejko, Joseph and Bzdu\v{s}ek, Tom\'{a}\v{s}},
  year            = {2023},
  howpublished    = {\url{https://github.com/patrick-lenggenhager/HyperCells}}
}

and at least one of the following references:

P. M. Lenggenhager, J. Maciejko, and T. Bzdušek, Non-Abelian hyperbolic band theory from supercells, Phys. Rev. Lett. (accepted), arXiv:2305.04945 (2023)

@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}},
  year            = {2023},
  journal         = {Phys. Rev. Lett. (accepted)},
  eprint          = {2305.04945},
  eprintType      = {arXiv},
  archivePrefix   = {arXiv},
  doi             = {10.48550/arXiv.2305.04945}
}

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

@phdthesis{Lenggenhager:PhDThesis,
  title           = {Emerging avenues in band theory: multigap topology and hyperbolic lattices},
  author          = {Lenggenhager, Patrick M.}, 
  year            = {2023},
  school          = {ETH Zurich}
}

as well as the following reference for the database of quotients of triangle groups with normal subgroups:

M. Conder, Quotients of triangle groups acting on surfaces of genus 2 to 101, https://www.math.auckland.ac.nz/~conder/TriangleGroupQuotients101.txt (2007)

@misc{Conder:2007,
  title           = {Quotients of triangle groups acting on surfaces of genus 2 to 101},
  author          = {Conder, Marston},
  year            = {2007},
  howpublished    = {\url{https://www.math.auckland.ac.nz/~conder/TriangleGroupQuotients101.txt}}
}

Feedback

For bug reports, feature requests and suggestions, please use the issue tracker.