Ground state entanglement constrains low-energy excitations

Understand

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.