周期图导出哈密顿量的泡利支撑不变量
Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians
- Quantum Center, University of Tennessee, Chattanooga（田纳西大学查塔努加分校量子中心）
- Department of Physics and Astronomy, University of Tennessee, Chattanooga（田纳西大学查塔努加分校物理与天文学系）
- Deloitte Consulting LLC（德勤咨询有限责任公司）
- Industrial and Systems Engineering, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校工业与系统工程）
- University of Tennessee, Chattanooga（田纳西大学查塔努加分校）
- University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于泡利分解的图不变量，证明周期图在格相容等价下的不变性，并扩展至非周期图与准晶体，为比较量子系统提供新机制。
AI中文摘要：
我们引入了一种图不变量，该不变量通过从局部图邻域导出的哈密顿量的泡利分解获得。给定一个以根节点为中心的h跳邻域，我们构造一个局部邻接算子，将其嵌入到公共希尔伯特空间维度中，并将其泡利支撑集定义为具有非零系数的泡利字符串的集合。对于周期图，我们证明了在格相容图等价下的不变性，并在根分离假设下建立了逆命题。该框架自然扩展到由相关泡利支撑生成的李闭包、交换子和嘉当型结构。我们进一步讨论了具有有限局部复杂性的非周期图的扩展，并与准晶体的切割投影模型（尤其是彭罗斯镶嵌）建立了联系。从量子信息的角度来看，所得不变量提供了基于图的哈密顿量的算子理论描述，并为通过泡利支撑数据比较基于图的量子系统提供了一种新机制。
英文摘要：
We introduce a graph invariant obtained from Pauli decompositions of Hamiltonians derived from local graph neighborhoods. Given a rooted h-hop neighborhood, we construct a local adjacency operator, embed it into a common Hilbert space dimension, and define its Pauli-support set as the collection of Pauli strings appearing with nonzero coefficients. For periodic graphs, we prove invariance under lattice-compatible graph equivalence and establish converse results under root-separation hypothesis. The framework naturally extends to Lie closures, commutants, and Cartan-type structures generated by the associated Pauli supports. We further discuss extensions to aperiodic graphs with finite local complexity and make connections to cut-and-project models of quasicrystals and notably, Penrose tilings. From a quantum information perspective, the resulting invariants provide a operator-theoretic description of graph-based Hamiltonians and offer a new mechanism for comparing graph-based quantum systems through Pauli-support data.
