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A family of two-dimensional AKLT models with a spectral gap above the ground state

Mathematical Physics & Probability

Speaker: Bruno Nachtergaele, UC Davis
Location: 2112 MSB
Start time: Wed, Jan 30 2019, 4:10PM

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).