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Fusion rules from entanglement

Shi, Bowen and Kato, Kohtaro and Kim, Isaac H. (2020) Fusion rules from entanglement. Annals of Physics, 418 . Art. No. 168164. ISSN 0003-4916. https://resolver.caltech.edu/CaltechAUTHORS:20200409-144558293

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Abstract

We derive some of the axioms of the algebraic theory of anyon (Kitaev, 2006) from a conjectured form of entanglement area law for two-dimensional gapped systems. We derive the fusion rules of topological charges and show that the multiplicities of the fusion rules satisfy these axioms. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy of a disk-like region, this term is shown to be equal to ln D, where D is the total quantum dimension of the underlying anyon theory. These derivations are rigorous and follow from the entanglement area law alone. More precisely, our framework starts from two local entropic constraints which are implied by the area law. From these constraints, we prove what we refer to as the “isomorphism theorem.” The existence of superselection sectors and fusion multiplicites follow from this theorem, even without assuming anything about the parent Hamiltonian. These objects and the axioms of the anyon theory are shown to emerge from the structure and the internal self-consistency relations of the information convex sets.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aop.2020.168164DOIArticle
https://arxiv.org/abs/1906.09376arXivDiscussion Paper
ORCID:
AuthorORCID
Shi, Bowen0000-0002-0689-9964
Kato, Kohtaro0000-0003-3317-2004
Additional Information:© 2020 Published by Elsevier Inc. Received 29 August 2019, Accepted 31 March 2020, Available online 8 April 2020. BS wishes to thank Yilong Wang for a discussion on possible obstruction of the categorification of fusion rings. BS is supported by the National Science Foundation under Grant No. NSF DMR-1653769. IK's research at Perimeter Institute was supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. IK also acknowledges support from IBM T. J. Watson research center as well as Simons foundation. KK is supported by the Institute for Quantum Information and Matter (IQIM) at Caltech, which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907).
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFDMR-1653769
Industry CanadaUNSPECIFIED
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Thomas J. Watson Research CenterUNSPECIFIED
Simons FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
Subject Keywords:Anyon; Fusion rule; Quantum entanglement; Quantum phases; Topological order; Topological entanglement entropy
Record Number:CaltechAUTHORS:20200409-144558293
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200409-144558293
Official Citation:Bowen Shi, Kohtaro Kato, Isaac H. Kim, Fusion rules from entanglement, Annals of Physics, Volume 418, 2020, 168164, ISSN 0003-4916, https://doi.org/10.1016/j.aop.2020.168164. (http://www.sciencedirect.com/science/article/pii/S000349162030097X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102466
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Apr 2020 21:50
Last Modified:09 Jun 2020 19:20

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