Momentum-space entanglement after smooth quenches

TL;DR

This paper calculates the momentum-space entanglement generated after smooth mass quenches in free quantum field theories, revealing dependence on quench speed, profile, and particle type, and connecting results to a Generalized Gibbs Ensemble.

Contribution

It provides closed-form expressions for entanglement and Rényi entropies after smooth quenches, highlighting differences between bosonic and fermionic fields and linking to thermalization predictions.

Findings

Entanglement is greater for light modes and fast quenches in bosons.

Adiabatic quenches do not produce entanglement.

Fermionic entanglement shows a critical quench amplitude and peaked momentum distribution.

Abstract

We compute the total amount of entanglement produced between momentum modes at late times after a smooth mass quench in free bosonic and fermionic quantum field theories. The entanglement and R\'enyi entropies are obtained in closed form as a function of the parameters characterizing the quench protocol. For bosons, we show that the entanglement production is more significant for light modes and for fast quenches. In particular, infinitely slow or adiabatic quenches do not produce any entanglement. Depending on the quench profile, the decrease as a function of the quench rate $\delta t$ can be either monotonic or oscillating. In the fermionic case the situation is subtle and there is a critical value for the quench amplitude above which this behavior is changed and the entropies become peaked at intermediate values of momentum and of the quench rate. We also show that the results agree with the predictions of a Generalized Gibbs Ensemble and obtain explicitly its parameters in terms of the quench data.