The AKLT model on a hexagonal chain is gapped
Quantum Physics
2020-01-08 v1 Statistical Mechanics
Strongly Correlated Electrons
Mathematical Physics
math.MP
Abstract
In 1987, Affleck, Kennedy, Lieb, and Tasaki introduced the AKLT spin chain and proved that it has a spectral gap above the ground state. Their concurrent conjecture that the two-dimensional AKLT model on the hexagonal lattice is also gapped remains open. In this paper, we show that the AKLT Hamiltonian restricted to an arbitrarily long chain of hexagons is gapped. The argument is based on explicitly verifying a finite-size criterion which is tailor-made for the system at hand. We also discuss generalizations of the method to the full hexagonal lattice.
Cite
@article{arxiv.1904.01043,
title = {The AKLT model on a hexagonal chain is gapped},
author = {Marius Lemm and Anders Sandvik and Sibin Yang},
journal= {arXiv preprint arXiv:1904.01043},
year = {2020}
}
Comments
17 pages; 4 figures; 2 tables -- comments welcome