https://doi.org/10.1140/epjb/s10051-025-01021-1
Research – Solid State and Materials
Diagnosing chaos in a periodically driven Ising model with a ramping field via out-of-time-order correlation saturation
1
Department of Chemistry, Bar-Ilan University, 5290002, Ramat-Gan, Israel
2
Optics and Quantum Information Group, The Institute of Mathematical Sciences, 600113, Chennai, India
3
Homi Bhabha National Institute, 400085, Mumbai, India
4
Department of Physics, Indian Institute of Technology (Banaras Hindu University), 221005, Varanasi, India
5
Department of Physics, Indian Institute of Technology Tirupati, 517619, Tirupati, India
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
29
March
2025
Accepted:
31
July
2025
Published online:
13
August
2025
Abstract
The dynamic region of out-of-time-ordered correlators (OTOCs) serves as a powerful indicator of chaos in classical and semiclassical systems, capturing the characteristic exponential growth. However, in spin systems, the dynamic region of OTOCs does not reliably quantify chaos as both integrable and chaotic systems display similar behavior. Instead, we utilize the saturation behavior of OTOCs to differentiate between chaotic and integrable regimes. In integrable systems, the saturation region of OTOCs exhibits oscillatory behavior, while in chaotic systems, it shows a stable saturation. To evaluate this distinction, we investigate a time-dependent Ising spin system subjected to a linearly ramping transverse field, analyzing both integrable (without longitudinal field) and non-integrable (with longitudinal field) scenarios. This setup accelerates system ergodicity due to the introduction of an additional time scale within the system, enhancing chaotic dynamics in the non-integrable regime, and provides a compelling model for studying the interplay between integrability and chaos in quantum systems. To further support our findings, we investigate the level spacing distribution of time-dependent unitary operators, which effectively distinguishes chaotic from regular regions in our system and corroborates the results obtained from the saturation behavior of the OTOC. Additionally, we calculate a metric for the normalized Fourier spectrum of the OTOC which is dependent on the number of frequency components present to gain insights into the observed oscillations and its dependence on the ramping field.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
