Stacking and the triviality of invertible phases

Abstract:We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of irreducible sectors of the factors. This naturally leads to a faithful functor between the categories for each system and the category of the stacked system. We construct an intermediate `product' category which we then show is equivalent to the stacked system category. As a consequence, the sectors associated with an invertible state are trivial, namely, invertible states support no anyonic quasi-particles.

46 pages. v2: various clarifications, added details, and corrections

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

arXiv:2511.08382 [math-ph]

(or arXiv:2511.08382v2 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2511.08382 Focus to learn more arXiv-issued DOI via DataCite

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