# Entanglement Wedge Cross Section Growth During Thermalization

## TL;DR

This paper studies how the entanglement wedge cross section evolves during thermalization in holographic theories, revealing dependencies on spacetime dimensions, Lifshitz exponents, and temperature, with implications for non-local information measures.

## Contribution

It provides new analytic and numerical insights into the time evolution of EWCS during black hole formation across various holographic geometries, highlighting early-time scaling and growth velocities.

## Key findings

- Early-time EWCS scaling depends on Lifshitz exponent.
- EWCS exhibits linear growth with velocity related to entanglement velocity.
- Growth velocity depends on spacetime dimensions, exponents, and temperature.

## Abstract

Motivated by exploring the thermalization process in relativistic and non-relativistic holographic field theories after a non-local quench, we investigate some features in the time evolution of the entanglement wedge cross section (EWCS). This quantity is a possible holographic dual to some non-local information measures such as entanglement of purification. In particular, we focus on the time dependence of EWCS during black hole formation in D+2 dimensional AdS spacetime as well as geometries with Lifshitz and hyperscaling violating exponents. A combination of analytic and numerical results for large symmetric strip shaped boundary subregions shows that the scaling of EWCS at early times only depends on the Lifshitz exponent. In addition, this early growth regime is followed by a linear growth regime whose velocity depends on the dimensions of spacetime, the Lifshitz exponent, and the hyperscaling parameter. This velocity is the same as the entanglement velocity and for nontrivial dynamical exponent depends on the temperature of the final equilibrium state.