Local measures of entanglement in black holes and CFTs

We study the structure and dynamics of entanglement in CFTs and black holes. We use a local entanglement measure, the entanglement contour, which is a spatial density function for von Neumann entropy with some additional properties. The entanglement contour can be calculated in many 1+1d condensed matter systems and simple models of black hole evaporation. We calculate the entanglement contour of a state excited by a splitting quench, and find universal results for the entanglement contours of low energy non-equilibrium states in 2d CFTs. We also calculate the contour of a non-gravitational bath coupled to an extremal AdS(2) black hole, and find that the contour only has finite support within the bath, due to an island phase transition. The particular entanglement contour proposal we use quantifies how well the bath's state can be reconstructed from its marginals, through its connection to conditional mutual information, and the vanishing contour is a reflection of the protection of bulk island regions against erasures of the boundary state. (C) Copyright A. Rolph.

Automated summary

In this article, we study the entanglement structure and dynamics in CFTs and black holes, employing a local entanglement measure known as the entanglement contour. We calculate the entanglement contour for different systems, including 1+1-dimensional condensed matter systems and simplified models of black hole evaporation. Our findings reveal universal results for the entanglement contours in low energy non-equilibrium states of 2D CFTs and illustrate the presence of an island phase transition in the entanglement contour of a non-gravitational bath coupled to an extremal AdS(2) black hole.