Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part II. Cutting through the boundary

Journal of High Energy Physics

Jiaqi Lou¹  Ce Shen¹  Ling-Yan Hung² 

[1] Department of Physics and Center for Field Theory and Particle Physics, Fudan University;State Key Laboratory of Surface Physics, Fudan University;

关键词: Anyons;    Conformal Field Theory;    Chern-Simons Theories;    Topological Field Theories;   

DOI  :  10.1007/JHEP11(2019)168

来源: DOAJ

【 摘 要 】

Abstract We compute the entanglement entropy in a 2+1 dimensional topological order in the presence of gapped boundaries. Specifically, we consider entanglement cuts that cut through the boundaries. We argue that based on general considerations of the bulk- boundary correspondence, the “twisted characters” feature in the Renyi entropy, and the topological entanglement entropy is controlled by a “half-linking number” in direct analogy to the role played by the S-modular matrix in the absence of boundaries. We also construct a class of boundary states based on the half-linking numbers that provides a “closed-string” picture complementing an “open-string” computation of the entanglement entropy. These boundary states do not correspond to diagonal RCFT’s in general. These are illustrated in specific Abelian Chern-Simons theories with appropriate boundary conditions.

【 授权许可】

Unknown