Emergent Floquet ground state

Periodically driven quantum systems have attracted much attention in view of Floquet engineering, i.e., creating useful effective Hamiltonians by designing appropriate drivings. However, it remains nontrivial how to make their ground states in order to access useful functionalities of the effective Hamiltonians. Also, even if being created, such states are believed to break down eventually due to heating accompanied by external drivings according to the Floquet eigenstate thermalization hypothesis (ETH).

In this talk, we first provide exact-diagonalization results at finite systems, showing that the Floquet ETH can break down in the weak sense for sufficiently high-frequency drives in generic systems. Namely, there can be an exceptional state which does not obey the Floquet ETH and does not heat up to the infinite temperature in the long run. Second, using real-time dynamics approach, we show that the exceptional state, and its thermodynamic-limit counterpart, can be regarded as being adiabatically connected to the ground state of the time-averaged Hamiltonian when we slowly ramp up the driving period from zero.

We propose this adiabatic connection as the operational definition of the emergent Floquet ground state as well as an experimentally feasible procedure to prepare it.