Abstract
The authors show that Affleck-Kennedy-Lieb-Tasaki models on several lattices possess a nontrivial spectral gap, including models on the singly decorated diamond lattice and singly decorated kagome lattice and two other two-dimensional uniformly spin-2 models.
Highlights
The spin models constructed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) in 1987 [1,2] have prompted many further developments
We show that if one can determine that the gap of a weighted, finite-size AKLT Hamiltonian is larger than a certain threshold, the AKLT Hamiltonian on the square lattice is gapped in the thermodynamic limit
II, we review the method of proving the gap and provide more detailed discussions on how to obtain the lower bound on the energy gap
Summary
The spin models constructed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) in 1987 [1,2] have prompted many further developments. One key property for such phases of matter to be stable is the existence of a nonzero energy gap above the ground state. In one dimension, this was already solved in the original AKLT work [1] and general methods have been proposed and successfully applied [1,8,9].
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