Math Physics Seminar | Amanda Young, U. of Arizona, Tucson | "A gapped family of two-dimensional AKLT models" | Jadwin 343

Tue, Apr 23, 2019, 4:30 pm

The one-dimensional 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 conjectured that the two-dimensional version of their model on the hexagonal lattice also  exhibits a spectral gap. In this talk, we introduce a family of variants of the hexagonal AKLT model, defined by decorating each edge of the lattice with an AKLT chain of length n, and prove that these decorated models are gapped for all n ≥ 3.

 

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