Bruno Bertini (Author), Pasquale Calabrese (Author)

Abstract

We investigate the crossover of the entanglement entropy toward its thermal value in nearly integrable systems. We employ equations-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 toward 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 timescales 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 behavior, but it underestimates the initial slope of the entanglement entropy.

Keywords

neravnovesna statistična mehanika;prepletenostna entropija;nonequilibrium statistical mechanics;entanglement entropy;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 536.93
COBISS: 43059715 Link will open in a new window
ISSN: 2469-9950
Views: 371
Downloads: 286
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Other data

Secondary language: Slovenian
Secondary keywords: neravnovesna statistična mehanika;prepletenostna entropija;
Pages: str. 094303-1-094303-14
Volume: ǂVol. ǂ102
Issue: ǂiss. ǂ9
Chronology: 2020
DOI: 10.1103/PhysRevB.102.094303
ID: 12345756