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.

中文翻译：

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三角表面上拓扑量子自旋系统的计算机代码

我们从张量代数（例如量子自旋哈密顿量）中推导出哈密顿量的显式闭式矩阵表示。这些公式使我们能够对通用哈密顿系统进行软编码，并将输入数据系统化，以用于均匀结构化和非结构化哈密顿系统。结果是一个最佳的计算机代码，可以用作一个黑匣子，它接收某些输入文件并返回有关哈密顿量的光谱信息。该代码在 Kitaev 的复曲面模型上进行了测试，该模型部署在 0 和 1 的三角形表面上。我们代码的效率使这些模拟能够在普通笔记本电脑上执行。还提供了对应于属 2 的最小三角剖分的输入文件。