Floquet quantum critical points in (1+1) dimensions

Given a generic (1+1) dimensional quantum critical points which can be described by conformal field theory (CFT), we propose an analytically solvable setup to study the Floquet dynamics of the CFT, i.e., the dynamics of a CFT subject to a periodic driving. A complete phase diagram in the parameter space can be analytically obtained within our setup. We find two phases: the heating phase and the non-heating phase. In the heating phase, the entanglement entropy keeps growing linearly in time, indicating that the system keeps absorbing energy; in the non-heating phase, the entanglement entropy oscillates periodically in time, i.e., the system is not heated. At the phase transition, the entanglement entropy grows logarithmically in time in a universal way. Furthermore, we can obtain the critical exponent by studying the entanglement evolution near the phase transition. Mathematically, different phases (and phase transition) in a Floquet quantum critical point correspond to different types of Mobius transformations.