TY - JOUR

T1 - A class of two-dimensional AKLT models with a gap

AU - Abdul-Rahman, Houssam

AU - Lemm, Marius

AU - Lucia, Angelo

AU - Nachtergaele, Bruno

AU - Young, Amanda

N1 - Funding Information:
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.
Publisher Copyright:
© 2020 The Authors.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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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U2 - 10.1090/conm/741/14917

DO - 10.1090/conm/741/14917

M3 - Article

AN - SCOPUS:85082559298

SN - 0271-4132

VL - 741

SP - 1

EP - 21

JO - Contemporary Mathematics

JF - Contemporary Mathematics

ER -