Heating in integrable time-periodic systems

TL;DR

This paper explores how integrable systems under periodic driving can exhibit heating to infinite temperature, with energy absorption and effective temperatures diverging near certain frequencies, revealing universal asymptotic behaviors.

Contribution

It demonstrates that integrable time-periodic systems can heat to infinite temperature, providing a detailed analysis of the scaling behavior with system size and driving period.

Findings

Heating occurs near a frequency threshold where Floquet-Magnus expansion diverges.

Effective temperatures diverge as system size and driving period increase.

Steady state approaches infinite temperature with specific asymptotic scaling laws.

Abstract

We investigate a heating phenomenon in periodically driven integrable systems that can be mapped to free-fermion models. We find that heating to the high-temperature state, which is a typical scenario in non-integrable systems, can also appear in integrable time-periodic systems; the amount of energy absorption rises drastically near a frequency threshold where the Floquet-Magnus expansion diverges. As the driving period increases, we also observe that the effective temperatures of the generalized Gibbs ensemble for conserved quantities go to infinity. By the use of the scaling analysis, we reveal that in the limit of infinite system size and driving period, the steady state after a long time is equivalent to the infinite-temperature state. We obtain the asymptotic behavior $L^{-1}$ and $T^{-2}$ as to how the steady state approaches the infinite-temperature state as the system size $L$ and the driving period $T$ increase.