The AKLT Model on a Hexagonal Chain is Gapped

2019/04/01 by Marius Lemm, Anders W. Sandvik, Anders Sandvik +1
Physics and Astronomy · #Chain (unit) #Conjecture #Hamiltonian (control theory) #Hexagonal crystal system #Lattice (music) #Physics of Superconductivity and Magnetism #Quantum many-body systems #Topological Materials and Phenomena

paper · pdf · doi:10.1007/s10955-019-02410-4

openalex created_date 2019/04/11 · openalex publication_date 2019/10/26 · openalex updated_date 2026/08/05

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.

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