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An entropic invariant for 2D gapped quantum phases

Kato, Kohtaro and Naaijkens, Pieter (2018) An entropic invariant for 2D gapped quantum phases. . (Submitted)

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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. We show that the quantity 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 of the models. Our method circumvents some of the problems around extracting the topological entanglement entropy, allowing us to prove invariance under constant-depth quantum circuits.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:KK is thankful to Bowen Shi for helpful discussions and sharing his notes on calculation of information convex. KK acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907) and JSPS KAKENHI Grant Number JP16J05374. PN has received funding from the European Unions Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 657004.
Group:IQIM, 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
Record Number:CaltechAUTHORS:20190212-155447238
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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:03 Oct 2019 20:49

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