Heating in integrable time-periodic systems

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.

6+3 pages, 2+3 figures

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• Fibonacci steady states in a driven integrable quantum system
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Thermal and dissipative effects on the heating transition in a driven critical system
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• Generalized hydrodynamics of integrable quantum circuits
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
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• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
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