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arXiv · 1901.09297

A class of two-dimensional AKLT models with a gap

Houssam Abdul-Rahman·Marius Lemm·Angelo Lucia·Bruno Nachtergaele·Amanda Young
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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 $n \geq 3$.

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Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele, Amanda Young. 2019-01-27. A class of two-dimensional AKLT models with a gap. https://doi.org/10.1090/conm%2F741%2F14917

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