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

TL;DR

This paper investigates how local projective measurements influence quantum dynamics in a non-integrable Bose-Hubbard model, revealing a measurement-induced phase transition characterized by a volume-to-area law change in entanglement.

Contribution

It provides the first detailed phase diagram of measurement-induced transitions in a non-integrable model using matrix product states and identifies universal scaling behavior.

Findings

Identifies a critical measurement rate causing a phase transition in entanglement scaling.

Shows a logarithmic growth of entanglement entropy at the critical point.

Finds that entanglement entropy distribution distinguishes different phases.

Abstract

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.