Thermal entanglement in conformal junctions

Abstract

We consider a quantum junction described by a 1+1-dimensional boundary conformal field theory (BCFT). Our analysis focuses on correlations emerging at finite temperature, achieved through the computation of entanglement measures. Our approach relies on characterizing correlation functions of twist fields using BCFT techniques. We provide non-perturbative predictions for the crossover between low and high temperatures. An intriguing interplay between bulk and boundary effects, associated with the bulk/boundary scaling dimensions of the fields above, is found. In particular, the entanglement entropy is primarily influenced by bulk thermal fluctuations, exhibiting extensiveness for large system sizes with a prefactor independent of the scattering properties of the defect. In contrast, negativity is governed by fluctuations across the entangling points only, adhering to an area law; its value depends non-trivially on the defect, and it diverges logarithmically as the temperature is decreased. To validate our predictions, we numerically check them for free fermions on the lattice, finding good agreement.