Stability of the Spectral Gap and Ground State Indistinguishability for a Decorated AKLT Model

Abstract

We use cluster expansion methods to establish local the indistiguishability of the finite volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our estimates imply that the model satisfies local topological quantum order, and so, the spectral gap above the ground state is stable against local perturbations.

Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

“…It is also well-established for Kitaev's quantum double models [16,34] and the Levin-Wen string-net model [37,57]. LTQO was recently also shown to hold for the AKLT model on a decorated hexagonal lattice [40].…”