Stacking and the triviality of invertible phases

Bachmann, Sven, Getz, Alan, Naaijkens, Pieter ORCID: https://orcid.org/0000-0001-5670-243X and Wray, Naomi 2026. Stacking and the triviality of invertible phases. Annales Henri Poincaré 10.1007/s00023-026-01768-y

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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.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Computational & Mathematical Sciences Schools > Mathematics
Publisher:	Springer
ISSN:	1424-0637
Date of First Compliant Deposit:	20 October 2026
Date of Acceptance:	20 October 2026
Last Modified:	20 Oct 2026 11:30
URI:	https://orca.cardiff.ac.uk/id/eprint/190336

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