Topological entanglement entropy of a Bose-Hubbard spin liquid

Abstract

The Landau paradigm of classifying phases by broken symmetries was shown to be incomplete when it was realized that different quantum-Hall states can only be distinguished by more subtle, topological properties1. The role of topology as an underlying description of order has since branched out to include topological band insulators and certain featureless gapped Mott insulators with a topological degeneracy in the ground-state wavefunction. Despite intense work, very few candidates for such topologically ordered ′spin liquids′ exist. The main difficulty in finding systems that harbour spin-liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we describe a spin-liquid phase in a Bose-Hubbard model on the kagome lattice, and determine its topological order directly by means of a measure known as topological entanglement entropy. We thus identify a non-trivial spin liquid through its entanglement entropy as a gapped ground state with emergent Z 2 gauge symmetry. © 2011 Macmillan Publishers Limited. All rights reserved.