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

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→ 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 $k → infty$ limit of the entropies after taking the large-party limit for this particular example.