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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 with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved 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 is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras from the local ground states.

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Zhengwei Liu, Zishuo Zhao. 2025-10-23. Topological Orders from Reflection Positive Frustration-free Hamiltonians. https://arxiv.org/abs/2510.20662

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