Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands

TL;DR

This paper investigates how graybody factors, modeled as a partially transmitting interface, influence entanglement entropy and the formation of entanglement islands in free fermion systems, revealing a monotonic dependence on transmission properties.

Contribution

It introduces a model for graybody factors affecting entanglement islands using free fermions with a semi-transparent interface, providing new insights into their impact on entanglement structure.

Findings

Entanglement entropy varies monotonically with interface transmission.

Partial transmission affects the location of entanglement islands.

Results connect graybody factors to entanglement structure in black hole models.

Abstract

We study the entanglement entropy of free fermions in 2d in the presence of a partially transmitting interface that splits Minkowski space into two half-spaces. We focus on the case of a single interval that straddles the defect, and compute its entanglement entropy in three limits: Perturbing away from the fully transmitting and fully reflecting cases, and perturbing in the amount of asymmetry of the interval about the defect. Using these results within the setup of the Poincar\'e patch of AdS$_2$ statically coupled to a zero temperature flat space bath, we calculate the effect of a partially transmitting AdS$_2$ boundary on the location of the entanglement island region. The partially transmitting boundary is a toy model for black hole graybody factors. Our results indicate that the entanglement island region behaves in a monotonic fashion as a function of the transmission/reflection coefficient at the interface.