Investigation of quantum chaos in local and non-local Ising models

TL;DR

This paper explores how local and non-local Ising models exhibit quantum chaos, showing that non-local interactions promote faster chaos onset and more complex dynamics, analyzed through energy level statistics and Krylov complexity.

Contribution

It provides a comparative analysis of chaos signatures in local versus non-local Ising models, highlighting the impact of non-local couplings on dynamical complexity and chaos indicators.

Findings

Non-local interactions lead to faster chaos onset.

Energy level spacing ratios reveal transition from integrability to chaos.

Krylov complexity peaks and plateaus characterize chaotic regimes.

Abstract

We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit integrable or chaotic dynamics contingent on interaction strengths and field parameters, systems with non-local interactions generally display a stronger propensity toward chaos, even when the non-local couplings are weak. By examining the distribution of energy level spacings through the level spacing ratio, we delineate the transition from integrable to chaotic regimes and characterize the emergence of quantum chaos in these systems. Our analysis demonstrates that non-local couplings facilitate faster operator spreading and more intricate dynamical behavior, enabling these systems to approach maximal chaos more readily than their local counterparts. Additionally, we analyze Krylov complexity as a dynamical probe of chaos, observing a characteristic peak followed by a plateau at late times in chaotic regimes. This behavior provides a quantitative means to distinguish between integrable and chaotic phases, with the growth rate and saturation level of the complexity serving as effective indicators. Our findings underscore the role of non-local interactions in accelerating the onset of chaos and modifying dynamical complexity in quantum spin chains.