Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model

TL;DR

This paper proves that a decorated AKLT model on hexagonal lattices maintains a stable spectral gap and local indistinguishability of ground states, indicating robustness of its topological order against local disturbances.

Contribution

It introduces a cluster expansion method to demonstrate local ground state indistinguishability and spectral gap stability in a decorated AKLT model with high decoration parameter.

Findings

Ground states are locally indistinguishable in finite volumes.

Spectral gap remains stable under local perturbations.

Model satisfies local topological quantum order (LTQO).

Abstract

We use cluster expansions to establish local 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 (LTQO), and so the spectral gap above the ground state is stable against local perturbations.