Metastability and discrete spectrum of long-range systems

Year: 2021

Authors: Defenu N.

Autors Affiliation: Swiss Fed Inst Technol, Inst Theoret Phys, CH-8093 Zurich, Switzerland.

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 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 Poincare 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.

Journal/Review: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Volume: 118 (30)      Pages from: e2101785118-1  to: e2101785118-12

More Information: Useful discussions with T. Enss, G. Folena, G. Gori, G. M. Graf, M. Kastner, A. Lerose, G. Morigi, S. Pappalardi, S. Ruffo, M. Salmhofer, and A. Trombettoni are gratefully acknowledged. This work is supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster).
KeyWords: quantum thermodynamics; equilibration; long-range interactions
DOI: 10.1073/pnas.2101785118

Citations: 29
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