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arXiv · 1912.12964

A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces

Yingkai Liu·Emil Prodan
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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 code deployed on triangulated surfaces of genus 0 and 1. The input file corresponding to the minimal triangulation of genus 2 is also supplied.

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Yingkai Liu, Emil Prodan. 2019-12-30. A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces. https://doi.org/10.1142/s0129183120500916

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