# Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

## TL;DR

This paper develops a perturbative approach using branch point twist fields to analyze the time evolution of entanglement entropy after a mass quench in the 1+1D Ising field theory, with results confirmed by lattice simulations.

## Contribution

It introduces a novel perturbative method for calculating entanglement dynamics in massive quantum field theories post-quench, extending the twist field approach to time-dependent problems.

## Key findings

- Linear growth of Rènyi entropies at large times
- Presence of oscillatory contributions with frequency 2m
- Good agreement with lattice numerical results

## Abstract

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass $m_0$ to final mass $m$. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the R\'enyi entropies at large times $mt\gg 1$ emerges from a perturbative calculation at second order. We also show that the R\'enyi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency $2m$ and amplitude proportional to $(mt)^{-3/2}$. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points.