Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions

TL;DR

This paper studies the universal and model-dependent multifractal properties of wave-functions in 1D quantum circuits with measurements, revealing a universal order parameter for measurement-induced phase transitions.

Contribution

It introduces a universal sub-leading term in participation entropy that acts as an order parameter for phase transitions, supported by numerical and analytical evidence.

Findings

Participation entropy exhibits model-dependent multifractal scaling.

Universal sub-leading term distinguishes error correcting and Zeno phases.

Analytical interpretation links participation entropy to classical statistical models.

Abstract

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems, and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.