Holographic entropy inequalities and gapped phases of matter

TL;DR

This paper investigates holographic entropy inequalities in gapped phases of matter, showing their validity in systems with area-law entanglement and extending topological entanglement entropy concepts.

Contribution

It extends holographic entropy inequalities to gapped phases, generalizes topological entanglement entropy, and proposes a new inequality for four-party quantum states.

Findings

All holographic entropy inequalities hold in systems with area-law entanglement.

Cyclic inequalities generalize the Kitaev-Preskill formula for topological entropy.

A candidate linear inequality for four-party quantum states is proposed.

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.