Prethermalization and thermalization in entanglement dynamics

Abstract

We investigate the crossover of the entanglement entropy towards its thermal value in nearly integrable systems. We employ equation of motion techniques to study the entanglement dynamics in a lattice model of weakly interacting spinless fermions after a quantum quench. For weak enough interactions we observe a two-step relaxation of the entanglement entropies of finite subsystems. Initially the entropies follow a nearly integrable evolution, approaching the value predicted by the Generalized Gibbs Ensemble (GGE) of the unperturbed model. Then, they start a slow drift towards the thermal stationary value described by a standard Gibbs Ensemble (GE). While the initial relaxation to the GGE is independent of the interaction, the slow drift from GGE to GE values happens on time scales proportional to the inverse interaction squared. For asymptotically large times and subsystem sizes the dynamics of the entropies can be predicted using a modified quasiparticle picture that keeps track of the evolution of the fermionic occupations caused by the integrability breaking. This picture gives a quantitative description of the results as long as the integrability-breaking timescale is much larger than the one associated with the (quasi) saturation to the GGE. In the opposite limit the quasiparticle picture still provides the correct late-time behaviour, but it underestimates the initial slope of the entanglement entropy.

Real-time evolution in the Hubbard model with infinite repulsion

“…[105,106], which could access the diffusion constant exactly. Another more difficult development concerns the use of our results as a starting point to set up an equations-of-motion scheme -similar to the one used to study prethermalization weakly interacting systems [72,[107][108][109][110] -to study the Hubbard model with large but finite interaction. A final extension of our calculations, motivated by recent cold-atom experiments [111] and by the results of Ref.…”

Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

“…Other open issues pertaining to the study of entanglement are (i) describe the full-time dynamics of the Rényi entropies based on a quasiparticle structure, (ii) clarify how integrability breaking affects the entanglement spreading [287], and (iii) incorporate the effects of dissipation in the quasiparticle picture [234,288]. Finally, another interesting direction is to investigate the entanglement spreading during the out-of-equilibrium dynamics with a time-dependent Hamiltonian, for instance, by using the approach developed in Ref.…”

Real-Time Evolution in the Hubbard Model with Infinite Repulsion

“…[97,98], which could access the diffusion constant exactly. Another more difficult development concerns the use of our results as a starting point to set up an equationsof-motion scheme -similar to the one used to study prethermalization weakly interacting systems [67,[99][100][101][102] -to study the Hubbard model with large but finite interaction. A final extension of our calculations, motivated by recent cold-atom experiments [103] and by the results of Ref.…”