Local measures of entanglement in black holes and CFTs

TL;DR

This paper introduces and applies a local entanglement measure called the entanglement contour to study the structure and dynamics of entanglement in conformal field theories and black holes, revealing universal behaviors and phase transitions.

Contribution

It proposes the entanglement contour as a local measure of entanglement and demonstrates its calculation in various models, including black hole evaporation and non-equilibrium states in 2d CFTs.

Findings

Universal entanglement contours in 2d CFTs after quenches

Finite support of the contour within the bath due to island phase transition

Contour's relation to reconstructability and protection of bulk regions

Abstract

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.