Metastability and discrete spectrum of long-range systems

TL;DR

This paper demonstrates that long-range interacting systems have a discrete spectrum up to the thermodynamic limit, explaining the emergence of long-lived quasi-stationary states and challenging traditional chaos assumptions in many-body quantum systems.

Contribution

It reveals the discrete spectral nature of long-range systems and links this to the existence of quasi-stationary states and Poincaré recurrence times, extending understanding of long-range quantum dynamics.

Findings

Spectrum remains discrete in long-range systems at large sizes

QSSs are connected to finite Poincaré recurrence times

Long-range interactions violate typical chaos spectral properties

Abstract

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 life-time, 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 presence of long-range interactions. In particular, the existence of QSSs may be traced back to the finiteness of Poincar\'e 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.