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arXiv · 2411.06648

Driven Critical Dynamics in Measurement-induced Phase Transitions

Wantao Wang·Shuo Liu·Jiaqiang Li·Shi-Xin Zhang·Shuai Yin
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Abstract

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 $S\propto \ln R$; while for increasing $p$ from the volume-law phase, $S$ satisfies $S\propto R^{1/r}$ 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.

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Wantao Wang, Shuo Liu, Jiaqiang Li, Shi-Xin Zhang, Shuai Yin. 2024-11-11. Driven Critical Dynamics in Measurement-induced Phase Transitions. https://arxiv.org/abs/2411.06648

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