Measurement-induced phase transitions in disordered fermions

TL;DR

This paper investigates how quenched disorder influences measurement-induced phase transitions in noninteracting fermionic systems, revealing that disorder does not alter the universal behavior or the existence of the transition in higher dimensions.

Contribution

It derives an effective field theory showing disorder modifies parameters but does not change the universality class of measurement-induced phase transitions.

Findings

Disorder enters the nonlinear sigma model only through parameter modifications.

In dimensions d>1, a transition exists between area x log law and area law phases.

In one dimension, only an area law phase is observed with no transition.

Abstract

Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder: in spatial dimensions d>1, a transition occurs between an area x log law phase and an area law phase, whereas in d=1, the system exhibits only an area law phase and no transition. Numerical results further demonstrate that both clean and disordered one-dimensional free fermions exhibit area-law behavior when the system size is large enough.