Topological Orders from Reflection Positive Frustration-free Hamiltonians

Zhengwei Liu; Zishuo Zhao

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arXiv · 2510.20662

Topological Orders from Reflection Positive Frustration-free Hamiltonians

Zhengwei Liu·Zishuo Zhao

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Abstract

We establish a framework based on reflection positivity for analyzing topologically ordered quantum spin systems and reconstructing their boundary algebras. For any reflection positive frustration-free Hamiltonian, we prove that the local topological quantum order (LTQO) condition of ground states on a disk holds, if and only if the ground state on the sphere obtained by gluing the disk with its reflection is nondegenerate. Furthermore, we show that Osterwalder-Schrader reconstruction produces the local net of boundary operator algebras from the local ground states, offering a constructive approach to topological holography through spatial reflection positivity.

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Zhengwei Liu, Zishuo Zhao. 2026-09-14. Topological Orders from Reflection Positive Frustration-free Hamiltonians. https://arxiv.org/abs/2510.20662

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