Exploring the Membrane Theory of Entanglement Dynamics

TL;DR

This paper extends the membrane theory of entanglement dynamics to more general settings, showing its robustness and applicability to various quench protocols, hydrodynamic couplings, and higher derivative corrections.

Contribution

It demonstrates that the membrane theory remains valid under broad generalizations, including coupling to hydrodynamics, joining quenches, and higher derivative gravity corrections.

Findings

Membrane couples geometrically to hydrodynamics in generic quenches.

Joining quenches are modeled by branes in the effective theory.

Higher derivative corrections do not alter the core structure of the theory.

Abstract

Recently an effective membrane theory valid in a "hydrodynamic limit" was proposed to describe entanglement dynamics of chaotic systems based on results in random quantum circuits and holographic gauge theories. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to hydrodynamics, joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to higher derivative gravity and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.