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.
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| 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 | ||||||||||||||||
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| Series Name: | Contemporary Mathematics | ||||||||||||||||
| Issue or Number: | 741 | ||||||||||||||||
| DOI: | 10.1090/conm/741/14917 | ||||||||||||||||
| 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: | 16 Nov 2021 18:43 |
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