Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models

TL;DR

This paper investigates the behavior of out-of-time-order correlations in Floquet Ising models, revealing characteristic departure times, power-law growth in dynamics, and linear saturation growth, with analytical and numerical methods applied.

Contribution

It provides a detailed analysis of OTOC regimes in Floquet Ising models, including exact solutions for integrable cases and numerical results for nonintegrable cases, highlighting the effects of observables' separation.

Findings

OTOCs depart from unity at a specific number of kicks depending on observable separation.

Power-law growth of OTOCs observed in both integrable and nonintegrable models.

Near saturation, OTOCs grow linearly with a very small rate.

Abstract

We study characteristic, dynamic, and saturation regimes of the out-of-time-order correlation (OTOC) in the constant field Floquet system with and without longitudinal field. In the calculation of OTOC, we take local spins in longitudinal and transverse directions as observables which are local and non-local in terms of Jordan-Wigner fermions, respectively. We use the exact analytical solution of OTOC for the integrable model (without longitudinal field term) with transverse direction spins as observables and numerical solutions for other integrable and nonintegrable cases. OTOCs generated in both cases depart from unity at a kick equal to the separation between the observables when the local spins in the transverse direction and one additional kick is required when the local spins in the longitudinal direction. The number of kicks required to depart from unity depends on the separation between the observables and is independent of the Floquet period and system size. In the dynamic region, OTOCs show power-law growth in both models, the integrable (without longitudinal field) as well as the nonintegrable (with longitudinal field). The exponent of the power-law increases with increasing separation between the observables. Near the saturation region, OTOCs grow linearly with a very small rate.