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.

30 pages, 2 figures

References in corpus (6)

• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Entanglement through conformal interfaces
• Page Curve and the Information Paradox in Flat Space
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• Modular Hamiltonians for the massless Dirac field in the presence of a defect

Cited by in corpus (5)

• Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands
• Holographic BCFT with a Defect on the End-of-the-World Brane
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Entropy of Radiation with Dynamical Gravity
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions