# Entanglement transition from variable-strength weak measurements

## TL;DR

Weak measurements can cause a quantum phase transition from an ergodic to a localized phase in many-body systems, with a critical measurement strength necessary for the transition, as demonstrated in a 1D quantum circuit model.

## Contribution

This work reveals a measurement-induced phase transition driven by variable-strength weak measurements in many-body systems, extending understanding beyond projective measurements.

## Key findings

- A critical measurement strength induces a transition from ergodic to localized phase.
- The phase boundary depends on measurement strength and probability.
- System remains ergodic below the critical measurement strength regardless of measurement probability.

## Abstract

We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement strength exceeds a critical value. We demonstrate this effect for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. As opposed to projective measurements describing a restricted class of open systems, the measuring device is modeled as a continuous Gaussian probe, capturing a large class of environments. By employing data collapse and studying the enhanced fluctuations at the transition, we obtain a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. These findings provide guidance for quantum engineering of many-body systems by controlling their environment.