Entanglement dynamics after quantum quenches in generic integrable systems

TL;DR

This paper provides an exact analytic description of entanglement entropy dynamics after quantum quenches in various integrable systems, combining quasiparticle pictures with Bethe ansatz solutions.

Contribution

It extends the quasiparticle approach to non-interacting and interacting integrable models, including the Lieb-Liniger gas, offering new exact results and insights.

Findings

Exact entanglement dynamics for non-interacting systems derived analytically.

Numerical validation of entanglement evolution in interacting spin chains.

Unique entanglement behavior in Lieb-Liniger model due to excitation velocity properties.

Abstract

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.