Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations

Qicheng Tang, W. Zhu

Published 2019-08-29Version 1

We study the effects of local projective measurements on the quantum quench dynamics. As a concrete example, one-dimensional Bose-Hubbard model is simulated by using matrix product state and time evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rates reach the critical values, we observe a logarithmic growth of entanglement entropy as the sub-system size or evolved time increases. This is akin to the character in the many-body localization, implying a general picture of the dynamical transitions separating quantum systems with different entanglement features. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases just as the case of disorder-induced many-body localization. This suggests that the different type entanglement phase transitions may be understood as a nonlocalized-to-localized transition. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated intervals, which is indicative of a single universality class and thus suggests a possible unified description of this transition.