Fermi's golden rule for heating in strongly driven Floquet systems

Abstract

We study heating dynamics in isolated quantum many-body systems driven periodically at high frequency and large amplitude. Combining the high-frequency expansion for the Floquet Hamiltonian with Fermi's golden rule (FGR), we develop a master equation termed the Floquet FGR. Unlike the conventional one, the Floquet FGR correctly describes heating dynamics, including the prethermalization regime, even for strong drives, under which the Floquet Hamiltonian is significantly dressed, and nontrivial Floquet engineering is present. The Floquet FGR depends on system size only weakly, enabling us to analyze the thermodynamic limit with small-system calculations. Our results also indicate that, during heating, the system approximately stays in the thermal state for the Floquet Hamiltonian with a gradually rising temperature.

Statistical mechanics of Floquet quantum matter: exact and emergent conservation laws

“…Under the periodic drive with the amplitude h x D above a sharp threshold, the system shows strong freezing, while below the threshold it is behaviour is consistent with Floquet thermalization to a locally infinite temperature state. This has been shown in figure 6 (for a detailed theory of heating below the threshold based on Fermi's golden Rule see [68][69][70]). Interestingly, as emphasized in the rightmost frame of the figure, the threshold value shows no perceptible dependence on the system-size L. The infinite drive-time limit ( T, as → ∞) is captured by taking the DEA in the Floquet basis (see, equation ( 22)).…”