Long-lived quasi-stationary states (QSSs) are a signature characteristic of long-range interacting systems both in the classical and in the quantum realms. Often, they emerge after a sudden quench of the Hamiltonian internal parameters and present a macroscopic lifetime, which increases with the system size. Despite their ubiquity, the fundamental mechanism at their root remains unknown. Here, we show that the spectrum of systems with power-law decaying couplings remains discrete up to the thermodynamic limit. As a consequence, several traditional results on the chaotic nature of the spectrum in many-body quantum systems are not satisfied in the presence of long-range interactions. In particular, the existence of QSSs may be traced back to the finiteness of Poincaré recurrence times. This picture justifies and extends known results on the anomalous magnetization dynamics in the quantum Ising model with power-law decaying couplings. The comparison between the discrete spectrum of long-range systems and more conventional examples of pure point spectra in the disordered case is also discussed.

长寿命准稳态 (QSS) 是经典和量子领域中远程相互作用系统的标志性特征。通常，它们在哈密顿内部参数突然淬灭后出现，并呈现出宏观寿命，随着系统尺寸的增加而增加。尽管它们无处不在，但其根源的基本机制仍然未知。在这里，我们展示了具有幂律衰减耦合的系统谱在热力学极限之前仍然是离散的。因此，在存在长程相互作用的情况下，关于多体量子系统中光谱混沌性质的几个传统结果并不令人满意。特别是，QSS 的存在可以追溯到庞加莱重复时间的有限性。这张图片证明并扩展了具有幂律衰减耦合的量子伊辛模型中异常磁化动力学的已知结果。还讨论了长程系统的离散谱与无序情况下更传统的纯点谱示例之间的比较。