A class of two-dimensional AKLT models with a gap

Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele, Amanda Young

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalContemporary Mathematics
Volume741
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Mathematics(all)

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