Dynamics of the Area Law of Entanglement Entropy

TL;DR

This paper investigates how the universal area law of entanglement entropy evolves under time-dependent perturbations in quantum field theories, providing a general formula and validating it through free field and holographic models.

Contribution

It derives a general formula for the first order correction to the entanglement entropy area law under time-dependent perturbations and confirms it with explicit free field and holographic calculations.

Findings

First order correction formula derived for time-dependent perturbations.

Explicit calculations in free field theories with time-dependent mass.

Qualitative and quantitative agreement with holographic models.

Abstract

We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.