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An entropic invariant for 2D gapped quantum phases

Kato, Kohtaro and Naaijkens, Pieter ORCID: 2020. An entropic invariant for 2D gapped quantum phases. Journal of Physics A: Mathematical and Theoretical 53 (8) , 085302. 10.1088/1751-8121/ab63a5

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We introduce an entropic quantity for two-dimensional quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator algebra defined on an annular region, which encodes the superselection sectors of the model. The quantity is calculable from local properties, and it is invariant under any constant-depth local quantum circuit, and thus an indicator of gapped quantum spin-liquids. We explicitly calculate the quantity for Kitaev's quantum double models, and show that the value is exactly same as the topological entanglement entropy (TEE) of the models. Our method circumvents some of the problems around extracting the TEE, allowing us to prove invariance under constant-depth quantum circuits.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: IOP Publishing
ISSN: 1751-8113
Date of First Compliant Deposit: 25 February 2020
Date of Acceptance: 18 December 2019
Last Modified: 08 Nov 2022 12:05

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