Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits

TL;DR

This paper investigates SU(2)-symmetric monitored quantum circuits, revealing a phase transition between volume-law entanglement and a critical phase, along with a spin-sharpening transition affecting measurement efficiency.

Contribution

It introduces the first analysis of entanglement and spin-sharpening transitions in SU(2)-symmetric monitored quantum circuits using exact numerics and a statistical-mechanics model.

Findings

Identified a transition between volume-law and critical phases with diffusive purification.

Discovered a spin-sharpening transition affecting measurement ability to determine total spin.

Showed non-Abelian symmetry leads to nontrivial entanglement scaling even in measurement-only limit.

Abstract

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.