The entanglement membrane in 2d CFT: reflected entropy, RG flow, and information velocity

TL;DR

This paper explores the membrane description of entanglement dynamics in 2d CFTs using holography, revealing the need for additional degrees of freedom for reflected entropy and how deformations lead to non-degenerate tensions, with extensions to higher dimensions.

Contribution

It introduces an extended membrane model for reflected entropy in 2d CFTs and demonstrates how relevant deformations produce a non-degenerate tension function, connecting to higher-dimensional cases.

Findings

Reflected entropy requires an additional degree of freedom in the membrane model.

Deformations of the CFT lead to a non-degenerate tension function.

The membrane description extends to higher dimensions for reflected entropy and information velocity.

Abstract

The time evolution of entanglement entropy in generic chaotic many-body systems has an effective description in terms of a minimal membrane, characterised by a tension function. For 2d CFTs, a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. In this paper we use holography to show that, in order to correctly capture the reflected entropy in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation of the CFT, dual to a planar BTZ black hole with scalar hair and with an interior Kasner universe. Finally, we also study the membrane description for reflected entropy and information velocity arXiv:1908.06993 in higher dimensions.