Measurement-induced criticality in $\mathbb{Z}_2$-symmetric quantum automaton circuits

TL;DR

This paper investigates how entanglement in $ ext{Z}_2$-symmetric quantum automaton circuits undergoes a phase transition driven by measurement rate, revealing a critical phase with unique universality class and dynamical properties.

Contribution

It introduces a detailed analysis of measurement-induced criticality in symmetric quantum circuits, linking entanglement phases to classical particle dynamics and universality classes.

Findings

Identification of a measurement-driven entanglement phase transition

Critical phase characterized by parity-conserving universality class

Entanglement entropy related to a two-species particle model

Abstract

We study entanglement dynamics in hybrid $\mathbb{Z}_2$-symmetric quantum automaton circuits subject to local composite measurements. We show that there exists an entanglement phase transition from a volume law phase to a critical phase by varying the measurement rate $p$. By analyzing the underlying classical bit string dynamics, we demonstrate that the critical point belongs to parity-conserving universality class. We further show that the critical phase with $p>p_c$ is related to the diffusion-annihilation process and is protected by the $\mathbb{Z}_2$-symmetric measurement. We give an interpretation of the entanglement entropy in terms of a two-species particle model and identify the coefficient in front of the critical logarithmic entanglement scaling as the local persistent coefficient. The critical behavior observed at $p\geq p_c$ and the associated dynamical exponents are also confirmed in the purification dynamics.