Suppression of Heating in Quantum Spin Clusters under Periodic Driving as a Dynamic Localization Effect

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Statistical mechanics

Background:

• Investigating energy absorption in quantum systems is crucial for understanding their dynamics.
• Ergodic clusters of interacting spins exhibit complex behavior under external fields.
• Periodic driving can lead to unique phenomena like heating or localization.

Purpose of the Study:

• To numerically and analytically study the heating process in interacting spin-1/2 clusters subjected to periodic magnetic field pulses.
• To identify conditions that suppress or induce heating in these quantum systems.
• To quantitatively determine the threshold for heating suppression and its relation to theoretical frameworks.

Main Methods:

• Numerical simulations of spin-1/2 clusters.
• Analytical investigations using perturbation theory.
• Analysis of the role of external magnetic field pulse strength and frequency.
• Examination of system size effects on heating dynamics.

Main Results:

• A critical threshold for the external magnetic field pulse strength was identified, below which heating is suppressed.
• This threshold decreases with increasing cluster size, vanishing in the thermodynamic limit.
• The heating suppression is quantitatively explained by the breakdown of the golden rule in second-order perturbation theory.
• The phenomenon of dynamic localization is identified as the underlying cause for heating suppression.

Conclusions:

• Heating in these driven quantum systems is not always guaranteed and can be controlled by external parameters.
• Dynamic localization provides a mechanism to prevent energy absorption in certain regimes.
• The findings are observable in systems with sufficiently large Hilbert spaces, offering experimental relevance.