Topological Orders from Reflection Positive Frustration-free Hamiltonians

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.

43 pages, 4 figures. Comments are welcome

Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2510.20662 [math-ph]

(or arXiv:2510.20662v4 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2510.20662 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.