A class of two-dimensional AKLT models with a gap
- Author(s): Nachtergaele, Bruno;
- Young, Amanda;
- Lucia, Angelo;
- Lemm, Marius;
- Abdul-Rahman, Houssam
- Editor(s): Abdul-Rahman, Houssam;
- Sims, Robert;
- Young, Amanda
- et al.
Published Web Locationhttps://doi.org/10.1090/conm/741/14917
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 $n\geq 3$.