Seeing topological entanglement through the information convex

In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.

Section: Introductionsupporting

confidence: 89%

Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I

Lou

Shen

Hung

2019

“…where S i,j is the matrix element of the modular group S-matrix. The vev or d j is called the quantum dimension of R j , which is known to be greater than or equal to one [56] (and see also appendix C in [57]),…”

Section: Chern-simons Theorymentioning

confidence: 99%

Towards a C-theorem in defect CFT

Kobayashi

Nishioka

Sato

et al. 2019

102

137

We explore a C-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate C-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a C-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.

“…There has been a lot of recent work exploring the effect topological boundaries have on the entanglement entropy of topological phases of matter [1,2,3,4,5,6,7]. In our last paper [5] we computed topological entanglement entropies of 2+1 dimensional topological order using Ishibashi states at the entanglement cut.…”

Section: Introductionmentioning

confidence: 99%

“…We will briefly conclude in section 4. Some details about Abelian Chern-Simons theories are relegated to the appendix A.…”

Section: Introductionmentioning

confidence: 99%

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

Shen

Lou

Hung

2019

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 halflinking numbers that provides a "closed-string" picture complementing an "openstring" 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. arXiv:1908.07700v1 [hep-th]