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An entropic invariant for 2D gapped quantum phases

Kato, Kohtaro and Naaijkens, Pieter (2020) An entropic invariant for 2D gapped quantum phases. Journal of Physics A: Mathematical and Theoretical, 53 (8). Art. No. 085302. ISSN 1751-8113. doi: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
Related URLs:
URLURL TypeDescription Paper
Kato, Kohtaro0000-0003-3317-2004
Naaijkens, Pieter0000-0001-5670-243X
Additional Information:© 2020 IOP Publishing Ltd. Received 27 August 2019; Accepted 18 December 2019; Accepted Manuscript online 18 December 2019; Published 28 January 2020. KK is thankful to Bowen Shi for helpful discussions and sharing his notes on calculation of the information convex. KK acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907) and JSPS KAKENHI Grant No. JP16J05374. PN has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant agreement No 657004 and the European Research Council (ERC) Consolidator Grant GAPS (No. 648913).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)JP16J05374
Marie Curie Fellowship657004
European Research Council (ERC)648913
Subject Keywords:quantum information, topologically ordered phase, operator algebra, topological entanglement entropy, quantum double
Issue or Number:8
Record Number:CaltechAUTHORS:20190212-155447238
Persistent URL:
Official Citation:Kohtaro Kato and Pieter Naaijkens 2020 J. Phys. A: Math. Theor. 53 085302
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92857
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:38
Last Modified:12 Jul 2022 19:50

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