Measurement-induced phase transitions in systems with diffusive dynamics

TL;DR

This paper investigates how coupling a 1+1d random Clifford circuit to diffusing particles alters the measurement-induced phase transition, leading to a new universality class with weaker Griffiths effects.

Contribution

It demonstrates that diffusive measurement density changes the universality class of MIPT, introducing diffusive correlations as a relevant perturbation.

Findings

Diffusive correlations modify the critical point of MIPT.

A new universality class for the phase transition is identified.

Weak Griffiths-like effects are observed due to rare space-time regions.

Abstract

The competition between scrambling and projective measurements can lead to measurement-induced entanglement phase transitions (MIPT). In this work, we show that the universality class of the MIPT is drastically altered when the system is coupled to a diffusing conserved density. Specifically, we consider a 1+1d random Clifford circuit locally monitored by classically diffusing particles (``measurers''). The resulting diffusive correlations in the measurement density are a relevant perturbation to the usual space-time random MIPT critical point, producing a new universality class for this phase transition. We find ``Griffiths-like'' effects due to rare space-time regions where, e.g., the diffusive measurers have a low or high density, but these are considerably weaker than the Griffiths effects that occur with quenched randomness that produce rare spatial regions with infinite lifetime.