Large-party limit of topological entanglement entropy in Chern-Simons theory

Abstract

We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group $G$ and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{dm,dn}$ torus link complements, which is a $d$-party pure quantum state, and analyze its large-party limit, i.e., $d\to \infty$ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of $\ln |Z_G|$, where $|Z_G|$ is the order of the center of the group $G$. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and $T_{d,dn}$ torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical ($k\to \infty$) limit of the entropies after taking the large-party limit for this particular example.

Matches with the published version. (16 pages, 1 figure, 1 table)

References in corpus (6)

• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• Semiclassical limit of topological Rényi entropy in $3d$ Chern-Simons theory
• Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
• Multipartite Entanglement Structure of Fibered Link States
• Entanglement in Typical States of Chern-Simons Theory
• Analyzing reduced density matrices in SU(2) Chern-Simons theory