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A class of two-dimensional AKLT models with a gap

  • Author(s): Nachtergaele, Bruno
  • Young, Amanda
  • Lucia, Angelo
  • Lemm, Marius
  • Abdul-Rahman, Houssam
  • Editor(s): Abdul-Rahman, Houssam
  • Sims, Robert
  • Young, Amanda
  • et al.
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 $n\geq 3$.

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