# Mathematics Colloquia and Seminars

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 variation of the two-dimensional AKLT model depending on an integer parameter 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 $n\geq 3$. (Joint work with H. Abdul-Rahman, M. Lemm, A. Lucia, and A. Young).