A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces
Strongly Correlated Electrons
2020-08-26 v2 Quantum Physics
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.
Keywords
Cite
@article{arxiv.1912.12964,
title = {A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces},
author = {Yingkai Liu and Emil Prodan},
journal= {arXiv preprint arXiv:1912.12964},
year = {2020}
}
Comments
optimized code can be executed on a laptop