Lindbladian PT phase transition: Emergence of continuous time crystals and critical exceptional points

Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated. However, there are only a few cases in which its condition for appearance has been fully elucidated. In this talk, we show that a Lindladian parity-time (PT) symmetry can generically produce persistent periodic oscillations, including dissipative continuous time crystals, in one-collective spin models. By making an analogy to non-reciprocal phase transitions, we demonstrate that a transition point from the oscillating phase is associated with spontaneous PT symmetry breaking and typically corresponds to a critical exceptional point. These results are established by proving that the Lindbladian PT symmetry at the microscopic level implies a non-linear PT symmetry and by performing a linear stability analysis near the transition point.