Holographic entropy inequalities and gapped phases of matter

Abstract

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the "cyclic inequalities" derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

20 pages, 4 figures. v2: section 4 rewritten, where all linear entropy (in)equalities satisfied by area-law systems are derived and an error in their relations to graph theory is corrected