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

TL;DR

This paper introduces the Floquet FGR, a master equation that accurately models heating in strongly driven Floquet systems, capturing prethermalization and enabling thermodynamic limit analysis.

Contribution

It develops the Floquet FGR, a novel approach combining high-frequency expansion and Fermi's golden rule for better heating dynamics modeling in driven quantum systems.

Findings

Floquet FGR accurately describes heating including prethermalization.

The method weakly depends on system size, allowing thermodynamic limit analysis.

Systems tend to stay in thermal states with rising temperature during heating.

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.