A computer code for topological quantum spin systems over triangulated surfaces

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.