TY - JOUR
T1 - A class of two-dimensional AKLT models with a gap
AU - Abdul-Rahman, Houssam
AU - Lemm, Marius
AU - Lucia, Angelo
AU - Nachtergaele, Bruno
AU - Young, Amanda
N1 - Publisher Copyright:
© 2020 The Authors.
PY - 2020
Y1 - 2020
N2 - 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 ≥ 3.
AB - 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 ≥ 3.
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U2 - 10.1090/conm/741/14917
DO - 10.1090/conm/741/14917
M3 - Article
AN - SCOPUS:85082559298
SN - 0271-4132
VL - 741
SP - 1
EP - 21
JO - Contemporary Mathematics
JF - Contemporary Mathematics
ER -