Entanglement through conformal interfaces

TL;DR

This paper analyzes how permeable conformal interfaces affect entanglement entropy in a (1+1)-dimensional CFT, revealing a permeability-dependent logarithmic scaling and topological-like sub-leading terms.

Contribution

It provides an analytical computation of entanglement entropy across permeable interfaces in c=1 CFT, introducing a permeability-dependent coefficient and topological entropy analogies.

Findings

Entanglement entropy scales logarithmically with system size.

The entropy coefficient depends on interface permeability via the dilogarithm.

Sub-leading terms relate to winding numbers, akin to topological entropy.

Abstract

We consider entanglement through permeable interfaces in the c=1 (1+1)-dimensional conformal field theory. We compute the partition functions with the interfaces inserted. By the replica trick, the entanglement entropy is obtained analytically. The entropy scales logarithmically with respect to the size of the system, similarly to the universal scaling of the ordinary entanglement entropy in (1+1)-dimensional conformal field theory. Its coefficient, however, is not constant but controlled by the permeability, the dependence on which is expressed through the dilogarithm function. The sub-leading term of the entropy counts the winding numbers, showing an analogy to the topological entanglement entropy which characterizes the topological order in (2+1)-dimensional systems.