10.57647/ijm2c.2027.1701.01

Investigation of Quantum Chaos in Local and Non-local Ising Models

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  • Reza Pirmoradian1,
  • Maryam Teymouri*1,
  • Elham Sadoogh1,
  • Negar AbolghasemiAzad1,
  • Mohammad Reza Lahooti1,
  • Zahra MohammadAli1,
  1. Faculty of Engineering, Ershad Damavand Institute of Higher Education, P.O.Box14676-86831, Tehran, Iran

Received: 24-07-2025

Revised: 07-12-2025

Accepted: 03-04-2026

Published in Issue 10-05-2026

Copyright (c) 2025 Reza Pirmoradian, Maryam Teymouri, Elham Sadoogh, Negar AbolghasemiAzad, Mohammad Reza Lahooti, Zahra MohammadAli (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Pirmoradian, R., Teymouri, M., Sadoogh, E., AbolghasemiAzad, N., Lahooti, M. R., & MohammadAli, Z. (2026). Investigation of Quantum Chaos in Local and Non-local Ising Models. International Journal of Mathematical Modelling & Computations. https://doi.org/10.57647/ijm2c.2027.1701.01
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Abstract

Time New Roman 10 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.

Keywords

  • Quantum chaos,
  • Thermalization,
  • Krylov Complexity,
  • Lanczos algorithm,
  • Level spacing,
  • Poisson and Wigner statistics Accepted manuscript
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