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

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 $p\ge p_c$ and the associated dynamical exponents are also confirmed in the purification dynamics.

15 pages, 12 figures

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• SYK meets non-Hermiticity II: measurement-induced phase transition
• Symmetry enriched phases of quantum circuits
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