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The conventional Kibble-Zurek scaling describes the scaling behavior in thedriven dynamics across a single critical region. In this paper, we study thedriven dynamics across an overlapping critical region, in which a criticalregion (Region-A) is overlaid by another critical region (Region-B). We developa hybridized Kibble-Zurek scaling (HKZS) to characterize the scaling behaviorin the driven process. According to the HKZS, the driven dynamics in theoverlapping region can be described by the critical theories for both Region-Aand Region-B simultaneously. This results in a constraint on the scalingfunction in the overlapping critical region. We take the quantum Ising chain inan imaginary longitudinal-field as an example. In this model, the criticalregion of the Yang-Lee edge singularity and the critical region of theferromagnetic-paramagnetic phase transition point overlap with each other. Wenumerically confirm the HKZS by simulating the driven dynamics in thisoverlapping region. The HKZSs in other models are also discussed.

Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region