Phase transitions in quasiperiodically driven quantum critical systems: Analytical results

In this paper, we analytically study phase transitions in quasiperiodically driven one-dimensional quantum critical systems that are described by conformal field theories (CFTs). The phase diagrams and phase transitions can be analytically obtained by using Avila's global theory in one-frequency quasiperiodic cocycles. Compared to previous works where the quasiperiodicity was introduced in the driving time and no phase transitions were observed [Wen et al., Phys. Rev. Res. 3, 023044 (2021)], here we propose a setup where the quasiperiodicity is introduced in the driving Hamiltonians. In our setup, one can observe the heating phases, nonheating phases, and phase transitions. The phase diagram as well as the Lyapunov exponents that determine the entanglement entropy evolution can be analytically obtained. In addition, based on Avila's theory, we prove there is no phase transition in the previously proposed setup of quasiperiodically driven CFTs [Wen et al., Phys. Rev. Res. 3, 023044 (2021)]. We verify our field theory results by studying the time evolution of entanglement entropy on lattice models.