The AKLT Model on a Hexagonal Chain is Gapped

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.


Published in:
Journal of Statistical Physics, 177, 6, 1077-1088
Year:
Dec 01 2019
ISSN:
0022-4715
1572-9613
Laboratories:




 Record created 2020-10-01, last modified 2020-10-29


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