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

Kai Ji1,2, Boris V Fine1,3

  • 1Skolkovo Institute of Science and Technology, Nobel Street 3, 143026 Moscow Region, Russia.

Physical Review Letters
|August 18, 2018
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We found a threshold pulse strength that suppresses heating in interacting spin systems. This threshold, dependent on cluster size, is linked to dynamic localization and the breakdown of the golden rule.

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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.