A computer code for topological quantum spin systems over triangulated surfaces

Yingkai Liu and Emil Prodan
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Yingkai Liu: Department of Physics, Yeshiva University, New York, 10016, USA
Emil Prodan: Department of Physics, Yeshiva University, New York, 10016, USA

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 07, 1-24

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.

Keywords: Toric code; quantum computation; anyonic model; many-body system (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500916

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