Integrability Breaking and Coherent Dynamics in Hermitian and Non-Hermitian Spin Chains with Long-Range Coupling

Abstract: Unraveling the mechanisms of ergodicity breaking in complex quantum systems is a central pursuit in nonequilibrium physics. In this work, we investigate a one-dimensional spin model featuring a tunable long-range hopping term, $H_{n}$, which introduces nonlocal interactions and bridges the gap between Hermitian and non-Hermitian regimes. Through a systematic analysis of level-spacing statistics, Krylov complexity, and entanglement entropy, we demonstrate that $H_{n}$ acts as a universal control parameter driving the transition from integrability to quantum chaos. Specifically, increasing the strength of $H_{n}$ induces a crossover from Poissonian to Gaussian Orthogonal Ensemble statistics in the Hermitian limit, and similarly triggers chaotic dynamics in the non-Hermitian case. Most remarkably, despite the onset of global chaos, we identify a tower of exact nonthermal eigenstates that evade thermalization. These states survive as robust quantum many-body scars, retaining low entanglement and coherent dynamics even under strong non-Hermitian perturbations. Our findings reveal a universal mechanism by which long-range and non-Hermitian effects reshape quantum ergodicity, offering new pathways for preserving quantum coherence in complex many-body systems.