Sharp detection of the onset of Floquet heating using eigenstate sensitivity

Abstract

Chaotic Floquet systems at sufficiently low driving frequencies are known to heat up to an infinite temperature ensemble in the thermodynamic limit. However at high driving frequencies, Floquet systems remain energetically stable in a robust prethermal phase with exponentially long heating times. We propose sensitivity (susceptibility) of Floquet eigenstates against infinitesimal deformations of the drive, as a sharp and sensitive measure to detect this heating transition. It also captures various regimes (timescales) of Floquet thermalization accurately. Particularly, we find that at low frequencies near the onset of unbounded heating, Floquet eigenstates are maximally sensitive to perturbations and consequently the scaled susceptibility develops a sharp maximum. We further connect our results to the relaxation dynamics of local observables to show that near the onset of Floquet heating, the system is nonergodic with slow glassy dynamics despite being nonintegrable at all driving frequencies.

15 pages, 7 figures, published in EPJB special issue dedicated to the memory of Amit Dutta

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Cited by in corpus (5)

• Geometric Floquet theory
• Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Floquet thermalization by power-law induced permutation symmetry breaking