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arXiv · 2511.08382

Stacking and the triviality of invertible phases

Sven Bachmann·Alan Getz·Pieter Naaijkens·Naomi Wray
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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.

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Sven Bachmann, Alan Getz, Pieter Naaijkens, Naomi Wray. 2025-11-11. Stacking and the triviality of invertible phases. https://arxiv.org/abs/2511.08382

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