GAP Package HyperCells

The current version of this package is version 0.9.1-beta, released on 2024-03-05. A getting-started guide for this and its sister package (HyperBloch) can be found here. For more information, please refer to the README file and the the package manual.

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

TGCellGraph objects and symmetric TGCell objects cannot be produced for cells without mirror symmetries, i.e., for quotients that act “chirally” on the surface.
Tests currently only succeed with GAP version 4.11 due to different but equivalent representation of certain groups elements as words in the generators.
Faces of TGCellGraph objects are currently not implemented for all cases, they are only implemented for tessellation and kagome graphs obtained using the TGTessellationGraph and TGKagomeGraph functions, respectively.

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, 10.5281/zenodo.10222598 (2023)

@misc{HyperCells,
  title           = {Hyper{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},
  doi             = {10.5281/zenodo.10222598},
  note            = {\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. 131, 226401 (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}},
  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}
}

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},
  doi             = {10.3929/ethz-b-000645370}
}

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.