Driven Critical Dynamics in Measurement-induced Phase Transitions

Measurement-induced phase transitions (MIPT), characterizing abrupt changes in entanglement properties in quantum many-body systems subjected to unitary evolution with interspersed projective measurements, have garnered increasing interest. In this work, we generalize the Kibble-Zurek (KZ) driven critical dynamics that has achieved great success in traditional quantum and classical phase transitions to MIPT. By linearly changing the measurement probability p to cross the critical point p_c with driving velocity R, we identify the dynamic scaling relation of the entanglement entropy S versus R at p_c. For decreasing p from the area-law phase, S satisfies Spropto ln R; while for increasing p from the volume-law phase, S satisfies Spropto R^1/r in which r=z+1/ν with z and ν being the dynamic and correlation length exponents, respectively. Moreover, we find that the driven dynamics from the volume-law phase violates the adiabatic-impulse scenario of the KZ mechanism. In spite of this, a unified finite-time scaling (FTS) form can be developed to describe these scaling behaviors. Besides, the dynamic scaling of the entanglement entropy of an auxiliary qubit S_Q is also investigated to further confirm the universality of the FTS form. By successfully establishing the driven dynamic scaling theory of this newfashioned entanglement transition, we bring a new fundamental perspective into MIPT that can be detected in fast-developing quantum computers.