Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results

Abstract

In this work, we study analytically the phase transitions in quasi-periodically 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 the previous works where the quasiperiodicity was introduced in the driving time and no phase transitions were observed [1], here we propose a setup where the quasiperiodicity is introduced in the driving Hamiltonians. In our setup, one can observe the heating phases, non-heating phases, and the 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 quasi-periodically driven CFTs [1]. We verify our field theory results by studying the time evolution of entanglement entropy on lattice models.