Floquet quantum criticality

It has recently been shown that quenched randomness, via the phenomenon of many-body localization, can stabilize dynamical phases of matter in periodically driven (Floquet) systems, with one example being discrete time crystals. This raises the question: what is the nature of the transitions between these Floquet many-body-localized phases, and how do they differ from equilibrium? We argue that such transitions are generically controlled by infinite randomness fixed points. By introducing a real-space renormalization group procedure for Floquet systems, asymptotically exact in the strong-disorder limit, we characterize the criticality of the periodically driven interacting quantum Ising model, finding forms of (multi-)criticality novel to the Floquet setting. We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.