A class of two-dimensional AKLT models with a gap

Abdul-Rahman, HoussamLemm, MariusLucia, AngeloNachtergaele, BrunoYoung, Amanda2020-10-012020-10-012020-10-01202010.1090/conm/741/14917https://infoscience.epfl.ch/handle/20.500.14299/172108The 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.A class of two-dimensional AKLT models with a gaptext::book/monograph::book part or chapter