Ground state entanglement constrains low-energy excitations

Abstract

For a general quantum many-body system, we show that its ground-state entanglement imposes a fundamental constraint on the low-energy excitations. For two-dimensional systems, our result implies that any system that supports anyons must have a nonvanishing topological entanglement entropy. We demonstrate the generality of this argument by applying it to three-dimensional quantum many-body systems, and showing that there is a pair of ground state topological invariants that are associated to their physical boundaries. From the pair, one can determine whether the given boundary can or cannot absorb point-like or line-like excitations.

4+6 pages, 22 figures, comments welcome; v2 typos and figures corrected, extended discussion on 3D invariant; v3 typos corrected, published version

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Cited by in corpus (9)

• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Anyonic Entanglement and Topological Entanglement Entropy
• Electromagnetic Duality and Entanglement Anomalies
• Seeing topological entanglement through the information convex
• Characterizing topological order by the information convex
• Entropic Topological Invariants in Three Dimensions
• Verlinde formula from entanglement
• Boundary topological entanglement entropy in two and three dimensions
• Remote detectability from entanglement bootstrap I: Kirby's torus trick