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A class of two-dimensional AKLT models with a gap

Abdul-Rahman, Houssam and Lemm, Marius and Lucia, Angelo and Nachtergaele, Bruno and Young, Amanda (2020) A class of two-dimensional AKLT models with a gap. In: Analytic Trends in Mathematical Physics. Contemporary Mathematics. No.741. American Mathematical Society , Providence, RI, pp. 1-21. ISBN 978-1-4704-4841-7. https://resolver.caltech.edu/CaltechAUTHORS:20200922-071519332

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Abstract

The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the hexagonal lattice exhibits a spectral gap. In this paper, we introduce a family of variants of the two-dimensional AKLT model depending on a positive integer n, which is defined by decorating the edges of the hexagonal lattice with one-dimensional AKLT spin chains of length n. We prove that these decorated models are gapped for all n ≥ 3.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/conm/741/14917DOIBook Table of Contents
http://www.ams.org/books/conm/741PublisherBook Table of Contents
https://arxiv.org/abs/1901.09297arXivDiscussion Paper
ORCID:
AuthorORCID
Lucia, Angelo0000-0003-1709-1220
Additional Information:© 2020 American Mathematical Society. This work arose from discussions during the follow-up workshop on Gapped Ground State Phases of Quantum Many-Body Systems to the 2018 Arizona School of Analysis and Mathematical Physics, organized by Robert Sims and two of the authors (H. A. and A. Y.) and supported by NSF Grant DMS-1800724. A. L. acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907). B. N. acknowledges support by the National Science Foundation under Grant DMS-1813149 and a CRM-Simons Professorship for a stay at the Centre de Recherches Mathématiques (Montréal) during Fall 2018, where part of this work was carried out.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFDMS-1800724
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
NSFDMS-1813149
Centre de Recherches Mathématiques (CRM)UNSPECIFIED
Series Name:Contemporary Mathematics
Issue or Number:741
Record Number:CaltechAUTHORS:20200922-071519332
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200922-071519332
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105464
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:22 Sep 2020 16:42
Last Modified:22 Sep 2020 16:42

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