Off-diagonal matrix elements of local operators in many-body quantum systems

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• Local observables in isolated quantum systems relax to asymptotic values determined by diagonal matrix elements.
• Off-diagonal matrix elements govern temporal fluctuations, response to perturbations, and relaxation dynamics.

Purpose of the Study:

• To investigate the statistical properties of off-diagonal matrix elements of local observables.
• To understand how these properties change in many-body systems tuned towards integrability.

Main Methods:

• Analysis of two families of interacting many-body systems with local interactions.
• Continuous tuning of models to probe the transition between integrable and nonintegrable regimes.
• Characterization of the distribution of off-diagonal matrix elements.

Main Results:

• In generic nonintegrable systems, off-diagonal matrix elements follow a Gaussian distribution centered at zero.
• As systems approach integrability, the distribution sharpens, resembling a combination of two Gaussians.
• The deviation from a Gaussian shape quantifies proximity to integrability.
• Scaling of the average magnitude of off-diagonal matrix elements with system size was determined.

Conclusions:

• The statistical distribution of off-diagonal matrix elements provides a sensitive probe of integrability in quantum many-body systems.
• Understanding these distributions is crucial for characterizing nonequilibrium dynamics and relaxation processes.