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

We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the 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 rate reaches the critical value, we observe a logarithmic growth of entanglement entropy as the subsystem size or evolved time increases. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases, similar to the case of disorder-induced many-body localization. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated sites, which is indicative of a single universality class and thus suggests a possible unified description of this transition.