Hierarchical relaxation dynamics in a tilted two-band Bose-Hubbard model

TL;DR

This paper investigates slow, hierarchical relaxation in a tilted two-band Bose-Hubbard model, revealing quantum chaos, eigenstate thermalization, and prethermalization phenomena through numerical and semiclassical analyses.

Contribution

It demonstrates the presence of hierarchical relaxation and prethermalization in a two-band Bose-Hubbard model, linking these phenomena to glassy dynamics and dynamical phase transitions.

Findings

Signatures of quantum chaos in the spectrum.

Eigenstate thermalization hypothesis validity in certain regimes.

Observation of prethermalized states and hierarchical relaxation.

Abstract

We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of the underlying mean-field trajectories. The observed prethermalization scenario can be attributed to different stages of glassy dynamics in the mode-time configuration space due to dynamical phase transition between ergodic and nonergodic trajectories.