Measurement-induced criticality in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>-symmetric quantum automaton circuits
Yiqiu Han, Xiao Chen
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 $p\ensuremath{\ge}{p}_{c}$ and the associated dynamical exponents are also confirmed in the purification dynamics.