Dynamical witnesses and universal behavior across chaos and non-ergodicity in the tilted Bose-Hubbard model

TL;DR

This paper investigates the transition from chaos to regularity in the tilted Bose-Hubbard model by analyzing dynamical observables, revealing a universal behavior and identifying the survival probability as the most robust chaos indicator.

Contribution

It introduces a universal scaling approach to characterize chaos-regularity transition in the tilted Bose-Hubbard model using multiple dynamical observables.

Findings

Survival probability is the most robust chaos indicator.

Entanglement entropy varies smoothly across the transition.

Scaled observables exhibit universal behavior across system sizes.

Abstract

Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized, the corresponding dynamical signatures across the transition to regularity remain less explored . In this work, we investigate this transition by analyzing the time evolution of the survival probability, the single-site entanglement entropy, and the half-chain imbalance. Our results reveal a clear hierarchy in the sensitivity of these observables: the relaxation value of the entanglement entropy varies smoothly as a function of the Hamiltonian parameters across the chaos-regular transition, while the imbalance exhibits a more pronounced distinction. Most notably, the survival probability emerges as the most robust indicator of the transition between chaos and regularity. When appropriately scaled, all three observables converge onto a common behavior as a function of the Hamiltonian parameters for different numbers of sites and bosons,enabling a universal characterization of the transition between chaotic and regular dynamics.