# Dynamics of logarithmic negativity and mutual information in smooth quenches

## TL;DR

This paper investigates how quantum correlations, specifically mutual information and logarithmic negativity, evolve over time in two different mass quench protocols in 2D free scalar theory, revealing propagation and oscillation behaviors.

## Contribution

It provides a detailed analysis of quantum correlation dynamics in smooth quenches, highlighting the effects of quench speed and protocol type on these correlations.

## Key findings

- Logarithmic negativity evolution aligns with relativistic particle propagation in ECP.
- Mutual information depends on both relativistic and slowly-moving particles in ECP.
- Quantum correlations oscillate post-quench in CCP, with suppression at large separations.

## Abstract

In this paper, we study how quantum correlation between subsystems changes in time by investigating time evolution of mutual information and logarithmic negativity in two protocols of mass quench. Hamiltonian in both protocols is for 2-dimensional free scalar theory with time-dependent mass: the mass in one case decreases monotonically and vanishes asymptotically (ECP), and that in the other decreases monotonically before t = 0, but increases monotonically afterward, and becomes constant asymptotically (CCP). We study the time evolution of the quantum correlations under those protocols in two different limits of the mass quench; fast limit and slow limit depending on the speed with which the mass is changed. We obtain the following two results: (1) For the ECP, we find that the time evolution of logarithmic negativity is, when the distance between the two subsystems is large enough, well-interpreted in terms of the propagation of relativistic particles created at a time determined by the limit of the quench we take. On the other hand, the evolution of mutual information in the ECP depends not only on the relativistic particles but also on slowly-moving particles. (2) For the CCP, both logarithmic negativity and mutual information oscillate in time after the quench. When the subsystems are well-separated, the oscillation of the quantum correlations in the fast limit is suppressed, and the time evolution looks similar to that under the ECP in the fast limit.