Mesoscopic Regimes of Temporal Entanglement in Ergodic Quantum Systems

TL;DR

This paper investigates the temporal correlations in ergodic quantum systems, revealing a mesoscopic regime and limitations of random-circuit models at relevant timescales.

Contribution

It identifies a long mesoscopic regime in ergodic quantum dynamics and highlights deviations from random-circuit universality.

Findings

Integrable dynamics aligns with the quasiparticle picture.

Ergodic dynamics shows a mesoscopic regime with spectral reorganization.

Limitations of random-circuit models at experimentally relevant timescales.

Abstract

We study temporal correlations in interacting quantum systems through the influence functional of a half-infinite quantum Ising chain. Using R\'enyi entropies and temporal mutual information, we confirm that integrable dynamics is captured by the quasiparticle picture. In contrast, generic ergodic Hamiltonian dynamics exhibits pronounced deviations from random-circuit universality, and its generalization including a symmetry accounting for energy conservation. Instead, we find a long mesoscopic regime suggestive of a slow spectral reorganization of the influence functional. Our results reveal a rich temporal structure in generic Hamiltonian dynamics and point to limitations of existing random-circuit paradigms at experimentally and numerically relevant timescales.