Recurrence analysis of quantum many-body dynamics

TL;DR

This paper introduces recurrence analysis, a nonlinear time-series method, to study quantum many-body dynamics, revealing phase transitions and complex temporal behaviors in the transverse-field Ising model.

Contribution

It adapts classical recurrence analysis to quantum systems, enabling qualitative and quantitative insights into out-of-equilibrium quantum dynamics and phase transitions.

Findings

Recurrence plots show nearly periodic patterns in ferromagnetic phases.

Multiscale temporal structures emerge at criticality.

Recurrence quantifiers identify critical field strength without prior knowledge.

Abstract

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a nonlinear time-series analysis framework long established for classical dynamical systems - to investigate correlated quantum many-body dynamics. Recurrence plots provide a qualitative fingerprint of simulated or experimental data, while recurrence quantification analysis extracts corresponding numerical descriptors. Applying this framework to quenches from the paramagnetic ground state in the one-dimensional transverse-field Ising model, we observe a clear progression in the recurrence plots of two-site correlations: nearly periodic patterns in the deeply ferromagnetic phase give way to multiscale temporal structures at criticality. Recurrence quantifiers further recover the critical field strength without prior knowledge of the model, establishing recurrence analysis as a versatile tool for characterizing quantum many-body dynamics, including unsupervised detection of quantum phase transitions.