Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Abstract
We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries on a tensor product of infinite-dimensional Hilbert spaces. We then show that any two anyon chains with the same symmetry category are related by a symmetry-compatible locality-preserving unitary after stabilizing with infinite-dimensional ancilla, showing that for a fixed fusion category, there is a single stable equivalence class of symmetry realizations on the lattice via anyon chains. As a corollary of our proof, we show that the physical boundary algebras of Levin-Wen type models are bounded spread isomorphic after stabilization if and only if they have the same bulk topological order.
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BibTeX
@misc{bunner2026universal,
title = {{Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces}},
author = {Ian Bunner and Corey Jones},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.21327},
eprint = {2605.21327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21327},
}
RIS
TY - UNPB
TI - Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
AU - Ian Bunner
AU - Corey Jones
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2605.21327
UR - https://arxiv.org/abs/2605.21327
AB - We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries on a tensor product of infinite-dimensional Hilbert spaces. We then show that any two anyon chains with the same symmetry category are related by a symmetry-compatible locality-preserving unitary after stabilizing with infinite-dimensional ancilla, showing that for a fixed fusion category, there is a single stable equivalence class of symmetry realizations on the lattice via anyon chains. As a corollary of our proof, we show that the physical boundary algebras of Levin-Wen type models are bounded spread isomorphic after stabilization if and only if they have the same bulk topological order.
ER -