Entanglement and topological interfaces

Abstract

In this paper we consider entanglement entropies in twodimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.

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

“…This can be compared with the discussion on CFT interfaces [11], which is characterized by chiral symmetry breaking. Here, from the perspective of topological phases, this has an immediate interpretation in terms of introducing an auxiliary topological phase that condenses in different ways to the phases A and B sandwiching the interface.…”

“…In particular, we work out in detail the Ishibashi states corresponding to gapped edges and interfaces. The important new ingredients compared to previous works such as [7,8,9,10,11,12,13] are that we provide a careful treatment of the matching of anyon charges across the interface using tools in anyon condensation. The anyon condensation picture allows us to generalize the results to include cases with ground state degeneracies, and also to non-Abelian systems.…”

“…Comparing with [33,14,11] where the interface preserves only a sub-algebra of those of phases A and B, it corresponds to the case in which C as a topological order condenses to A and B separately. In this case, these basis states |(a, b) αc correspond to the intertwiner state in equation (2.5) in [11], and the multiplicity is given precisely by the b matrix. We do not however impose the "modular invariance" condition.…”

Entanglement Entropy in CFT2

“…for topological interfaces in rational CFTs the corresponding interface operators were found in [16] and [17] by building off of the modular invariant projection operators constructed in [18]. When considering free fields, as in this work, the conditions can be written in terms of the creation and annihilation operators and can be solved by a coherent state anzatz.…”

Left-right entanglement entropy of Dp-branes

“…Some interesting generalizations of the LREE include its formulation in the more general context of arbitrary rational CFT [8], Ising model with interfaces [9], connection with level/rank duality [10]. More recent work [11] provided an alternative perspective on [8]; other interesting directions were discussed in [12].…”