Non equilibrium phase transitions and Floquet Kibble-Zurek scaling

Abstract

We study the slow crossing of non-equilibrium quantum phase transitions in periodically-driven systems. We explicitly consider a spin chain with a uniform time-dependent magnetic field and focus on the Floquet state that is adiabatically connected to the ground state of the static model. We find that this {\it Floquet ground state} undergoes a series of quantum phase transitions characterized by a non-trivial topology. To dinamically probe these transitions, we propose to start with a large driving frequency and slowly decrease it as a function of time. Combining analytical and numerical methods, we uncover a Kibble-Zurek scaling that persists in the presence of moderate interactions. This scaling can be used to experimentally demonstrate non-equilibrium transitions that cannot be otherwise observed.

7 pages, 3 figures, Supplemental Material. (In this last version, the one published in EPL, we provide a better discussion of the Floquet adiabatic theorem, the construction of the Floquet ground state as an adiabatic continuation and the nature of the phase transitions.)