SIM-GRAPH：对称相互作用的通用指南
SIM-GRAPH: A universal guide to symmetric interactions
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中文总结 AI 辅助
本文提出SIM-GRAPH方法，利用离散对称性将相互作用投影到对称子集以减少格点数，实现基态可观测量的指数级加速计算，并引入两种扩展以权衡计算成本与精度。
中文摘要 AI 辅助
对称性在整个物理学中扮演着核心角色，从离散晶格上的傅里叶分析到标准模型中基本粒子的分类。在有限量子系统中，对称性通常是离散的，例如反射对称性和旋转对称性。在此，我们提出SIM-GRAPH方法（对称伊辛模型-图约简与投影哈密顿量），该方法利用此类对称性来高效计算相互作用量子系统的基态可观测量。通过将所有相互作用投影到系统的一个对称子集上，该方法有效减少了格点数量，从而相较于标准精确对角化提供了指数级加速。此外，我们引入了两种扩展，拓宽了该方法的适用性，并允许在计算成本与精度之间进行可控的权衡。
英文摘要
Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.
发表机构
- Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）
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