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A computer code for topological quantum spin systems over triangulated surfaces

Author

Listed:
  • Yingkai Liu

    (Department of Physics, Yeshiva University, New York, 10016, USA)

  • Emil Prodan

    (Department of Physics, Yeshiva University, New York, 10016, USA)

Abstract

We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for uniformly structured as well as for un-structured Hamiltonians. The result is an optimal computer code that can be used as a black box that takes in certain input files and returns spectral information about the Hamiltonian. The code is tested on Kitaev’s toric model deployed on triangulated surfaces of genus 0 and 1. The efficiency of our code enables these simulations to be performed on an ordinary laptop. The input file corresponding to the minimal triangulation of genus 2 is also supplied.

Suggested Citation

  • Yingkai Liu & Emil Prodan, 2020. "A computer code for topological quantum spin systems over triangulated surfaces," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-24, July.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:07:n:s0129183120500916
    DOI: 10.1142/S0129183120500916
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