Non-Hermitian physics is a rapidly growing field that hosts rich intriguing phenomena with broad applications in photonics, condensed matter, and quantum information science. Yet, it is still unclear how to properly deal with the nonadiabatic dynamics in a driven non-Hermitian quantum system. Here, we introduce a novel theoretical framework based on time-dependent biorthogonal quantum formalism by redefining the associated state to ensure gauge-independent transition probabilities. Applying this framework to a linearly driven non-Hermitian system, our approach reveals universal power-law scaling of defect production that is consistent with the Kibble-Zurek mechanism in the adiabatic regime at exceptional points. In the fast quench regime, universal scaling behaviors are also found, which can be explained by the adiabatic-impulse approximation. Moreover, upon trespassing the $\mathcal{PT}$-broken region, the phenomenon of defect freezing, i.e., violation of adiabaticity, is observed.

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• Dynamic critical phenomena
• PT-symmetric quantum mechanics
• Quantum quench
• Dynamical systems
• Non-Hermitian systems