Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields

TL;DR

This paper investigates the time evolution of modular entropy and capacity in harmonic chains and scalar fields, comparing analytical results with quasiparticle models and exploring various quench protocols.

Contribution

It provides a detailed analytical study of the dynamics of entanglement capacity and modular entropy in time-dependent oscillator systems, including new insights into their behavior during quenches.

Findings

Derived the form of modular capacity for single oscillators and chains.

Compared dynamics with quasiparticle model predictions.

Analyzed effects of different boundary conditions and protocols.

Abstract

We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the discretization procedure, fit into field theory problems arising from quench phenomena or non-static spacetimes. First, we compare the dynamics of the modular and Renyi entropies and derive the form of the modular capacity for the single time-dependent oscillator as well as chains with bipartite decompositions. In the latter case we analyse distinguished periodicities during the evolution and the role of various boundary conditions. Next, we focus on the dynamics of the capacity (fluctuation) of entanglement. We compare the results obtained with the predictions of quasiparticles models; in particular, we obtain a theoretical value of the initial slope of the capacity for abrupt quenches. We study also continuous protocols with the frequency that vanishes at plus (and minus) infinity, including a model in which the frequency tends to the Dirac delta. All the above issues are discussed with the emphasis on the analytical methods.