A class of two-dimensional AKLT models with a gap

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 integern, which is defined by decorating the edges of the hexagonal lattice with one-dimensional AKLT spin chains of lengthn. We prove that these decorated models are gapped for alln≥3.


Published in:
Contemporary Mathematics, 1-21
Year:
2020
Publisher:
Providence, Rhode Island, American Mathematical Society
ISBN:
978-1-4704-4841-7
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 Record created 2020-10-01, last modified 2020-10-29


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