Topological entanglement negativity in Chern-Simons theories

TL;DR

This paper investigates the topological entanglement negativity in (2+1)D Chern-Simons theories, revealing how it depends on quasiparticles, ground states, and can distinguish Abelian from non-Abelian phases using a novel approach.

Contribution

It introduces a method using the replica trick and surgery to compute topological entanglement negativity in Chern-Simons theories on arbitrary manifolds, connecting with edge theory results.

Findings

Negativity depends on quasiparticles and ground states.

Distinguishes Abelian and non-Abelian theories.

Applicable to arbitrary (2+1)D manifolds.

Abstract

We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).