The AKLT model on a hexagonal chain is gapped

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.

17 pages; 4 figures; 2 tables -- comments welcome

References in corpus (3)

• Quantum computational capability of a 2D valence bond solid phase
• Spectral gaps of frustration-free spin systems with boundary
• Gapped PVBS models for all species numbers and dimensions

Cited by in corpus (6)

• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Improved local spectral gap thresholds for lattices of finite dimension
• Quantitatively improved finite-size criteria for spectral gaps
• Random translation-invariant Hamiltonians and their spectral gaps
• Fractional quantum Hall effect from frustration-free Hamiltonians
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems