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

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 Poincaré 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.

arXiv comment30 pages, 2 figures

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• Entanglement evolution after a global quench across a conformal defect
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• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line