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A class of two-dimensional AKLT models with a gap
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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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Improved local spectral gap thresholds for lattices of finite dimension
For frustration-free Hamiltonians on any finite-dimensional lattice, the minimum spectral gap of any rectangular region is O(γ + 1/t²) where t is the shortest side length, improving previous thresholds.
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