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

References in corpus (4)

• Area laws in quantum systems: mutual information and correlations
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• The Holographic Entropy Cone
• A new inequality for the von Neumann entropy

Cited by in corpus (13)

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• Majorana dimers and holographic quantum error-correcting codes
• Crossing versus locking: Bit threads and continuum multiflows
• Analysing causal structures with entropy
• Hypergraph min-cuts from quantum entropies
• Towards a complete classification of holographic entropy inequalities
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Strong subadditivity and holography
• On the completeness of contraction map proof method for holographic entropy inequalities
• Topological entanglement entropy meets holographic entropy inequalities