Entanglement spreading in one dimensional lattice systems

The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in  which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. 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.In the first part of the talk, we discuss the application of these ideas to several integrable models, both non-interacting and interacting  models, and test our results against numerical simulations. In the next part of the talk,  we will discuss how the entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts,  we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total  system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling.

Reference: [1] Ranjan Modak, Lorenzo Piroli, Pasquale Calabrese;  J. Stat. Mech. (2019) 093106
[2] Ranjan Modak, Vincenzo Alba, Pasquale Calabrese; arXiv:2004.08706 (2020)