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 pointlike or linelike excitations.

• Received 10 August 2015
• Revised 27 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.115139