Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems

In this work, we study analytically the phase transitions in quasi-periodically driven quantum critical systems that are described by conformal field theories (CFTs). Compared to previous works on quasi-periodically driven CFTs where no phase transitions were observed, here we propose a new setup where one can observe the heating phase, non-heating phase and the phase transition. The phase diagram as well as the Lyapunov exponents that determine the entanglement entropy evolution can be analytically obtained based on Avila's global theory.