Thermalization in the mixed-field Ising model: An occupation-number perspective

Area of Science:

• Statistical Mechanics
• Quantum Physics
• Condensed Matter Theory

Background:

• Occupation number is crucial for understanding thermalization and statistical distributions (Fermi-Dirac, Bose-Einstein, Boltzmann).
• In spin systems, it quantifies magnetization sublevel populations.
• Probing thermalization in isolated quantum spin models is challenging due to Hilbert space size.

Purpose of the Study:

• To investigate the onset of thermalization in a quantum spin-1 Ising model and its classical counterpart.
• To establish a quantitative criterion for ergodicity in interacting spin systems.
• To determine bounds for the approach to thermal equilibrium in quantum models.

Main Methods:

• Analyzed the occupation number dynamics in a 1D quantum spin-1 Ising model with transverse and longitudinal fields.
• Utilized the classical counterpart to overcome finite-size limitations in quantum simulations.
• Tracked individual spin dynamics on Bloch spheres and applied random matrix theory.

Main Results:

• Thermalization in the quantum model was assessed by the convergence of occupation number averages to microcanonical predictions.
• Classical ergodicity deviations were found to decay algebraically with system size (power-law scaling).
• This scaling provided a quantitative bound for the approach to thermal equilibrium in the quantum system.

Conclusions:

• The study establishes a link between classical ergodicity and quantum thermalization.
• Algebraic decay of classical ergodicity provides a practical method to bound quantum thermalization.
• The findings offer insights into the dynamics and equilibrium properties of isolated spin systems.