Axiomatization of the Levin--Wen Wave Function

Abstract:The Levin--Wen model provides a lattice realization of topological orders associated with a given unitary fusion category. A longstanding open problem is to characterize Levin--Wen ground-state wave functions intrinsically, without assuming a priori categorical symmetry data or a Hamiltonian. We address this by proposing six axioms on a family of wave functions defined on lattices at multiple scales. These axioms allow us to reconstruct the underlying unitary fusion category and prove that the resulting wave functions map to nonzero Levin--Wen ground-state vectors of the emergent category.

Mathematical Physics (math-ph); Quantum Algebra (math.QA); Quantum Physics (quant-ph)

arXiv:2608.21109 [math-ph]

(or arXiv:2608.21109v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2608.21109 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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