Stacking and the triviality of invertible phases

2025/11/11 by Sven Bachmann, Alan Getz, Bachmann, Sven +5
Physics and Astronomy · #Quantum many-body systems #Cold Atom Physics and Bose-Einstein Condensates #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.2511.08382

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.

Citations

• Haag Duality for 2D Quantum Spin Systems
• Mixed state topological order: operator algebraic approach
• Complete W*-categories
• An operator algebraic approach to symmetry defects and fractionalization
• Superselection sectors for posets of von Neumann algebras
• An index for invertible phases of two-dimensional quantum spin systems
• Many-body Fu-Kane-Mele index
• Classifying 2D topological phases: mapping ground states to string-nets
• Classification of the anyon sectors of Kitaev's quantum double model
• Anyons in an exactly solved model and beyond
• On the Structure of Modular Categories
• From subfactors to categories and topology II: The quantum double of tensor categories and subfactors
• Fault-tolerant quantum computation by anyons
• Quantum double finite group algebras and their representations
• Interpolation by type I factors and the flip automorphism
• Locality and the structure of particle states

Cited by

• The index of a pair of pure states and the interacting integer quantum Hall effect

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• Web of Non-invertible Dualities for (2+1) Dimensional Models with Subsystem Symmetries