Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians

Sarah Chehade; Andrew Vlasic; Rebekah Herrman; Rick Mukherjee

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arXiv · 2609.14209

Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians

Sarah Chehade·Andrew Vlasic·Rebekah Herrman·Rick Mukherjee

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Abstract

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.

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Sarah Chehade, Andrew Vlasic, Rebekah Herrman, Rick Mukherjee. 2026-09-13. Pauli Supported Invariants for Periodic Graphs-Derived Hamiltonians. https://arxiv.org/abs/2609.14209

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