Ground state entanglement constrains low-energy excitations

TL;DR

This paper establishes a fundamental link between ground-state entanglement and the nature of low-energy excitations in quantum many-body systems, revealing that topological entanglement entropy constrains the existence of anyons and boundary excitations.

Contribution

It introduces a general theoretical framework connecting ground-state entanglement to low-energy excitations and topological invariants in both two- and three-dimensional quantum systems.

Findings

Anyons require nonzero topological entanglement entropy in 2D.

Two topological invariants determine boundary excitation capabilities in 3D.

Ground-state entanglement constrains possible 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.