Research & Projects

Using the Kotecky-Preiss criterion for convergence of cluster expansions we prove the local indistiguishability of the finite-volume ground states for the AKLT model on the hexagonal (honeycomb) lattice. This proves this two-dimensional SU(2)-invariant groundstate possesses local topological quantum order (LTQO), which is one of the key assumptions needed to show the stability of the spectral gap above the groundstate against local perturbations. We also prove these results hold true for decorated hexagonal lattices for all decoration numbers d>0.

We show that a simple condition on the connectivity of a graph will lead to a long-range ordering in the AKLT model on a tree created from such a finite graph.