Metastability and discrete spectrum of long-range systems

Area of Science:

• Quantum Mechanics
• Statistical Physics
• Condensed Matter Physics

Background:

• Long-lived quasi-stationary states (QSSs) are observed in classical and quantum systems with long-range interactions.
• The underlying mechanism driving QSS formation, despite their prevalence after sudden parameter changes (quenches), remains poorly understood.
• System size typically correlates with the macroscopic lifetime of these QSSs.

Purpose of the Study:

• To elucidate the fundamental mechanism responsible for the emergence of QSSs in long-range interacting systems.
• To investigate the spectral properties of quantum systems with power-law decaying couplings.
• To connect spectral characteristics to the observed anomalous dynamics, particularly magnetization behavior.

Main Methods:

• Analysis of the energy spectrum for systems exhibiting power-law decaying couplings.
• Investigation of spectral properties up to the thermodynamic limit.
• Examination of the relationship between discrete spectra, Poincaré recurrence times, and QSS existence.

Main Results:

• Demonstrated that systems with power-law decaying couplings possess a discrete energy spectrum extending to the thermodynamic limit.
• Showed that this discrete spectrum violates traditional criteria for chaotic behavior in many-body quantum systems.
• Traced the existence of QSSs to the finiteness of Poincaré recurrence times, providing a mechanistic explanation.

Conclusions:

• The discrete nature of the spectrum in long-range interacting systems is the key to understanding QSS formation.
• This finding offers a theoretical basis for anomalous magnetization dynamics observed in models like the quantum Ising model with power-law couplings.
• Highlights the distinction between long-range interacting systems and disordered systems concerning spectral properties and QSS phenomena.