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arXiv:2110.10726 · Physical review. B./Physical review. B

Measurement-induced criticality in Z2 -symmetric quantum automaton circuits

Yiqiu Han, Xiao Chen

Published Feb 28, 2022• 23 citations
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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.

DOI
10.1103/physrevb.105.064306

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We study the entanglement dynamics of quantum automaton (QA) circuits in the presence of U(1) symmetry. We find that the second Rényi entropy grows diffusively with a logarithmic correction as tln⁡t , saturating the bound established by Huang \cite{Huang_2020}. Thanks to the special feature of QA circuits, we understand the entanglement dynamics in terms of a classical bit string model. Specifically, we argue that the diffusive dynamics stems from the rare slow modes containing extensively long domains of spin 0s or 1s. Additionally, we investigate the entanglement dynamics of monitored QA circuits by introducing a composite measurement that preserves both the U(1) symmetry and properties of QA circuits. We find that as the measurement rate increases, there is a transition from a volume-law phase where the second Rényi entropy persists the diffusive growth (up to a logarithmic correction) to a critical phase where it grows logarithmically in time. This interesting phenomenon distinguishes QA circuits from non-automaton circuits such as U(1)-symmetric Haar random circuits, where a volume-law to an area-law phase transition exists, and any non-zero rate of projective measurements in the volume-law phase leads to a ballistic growth of the Rényi entropy.
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We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two distinct dynamical phases, one characterized by a volume-law scaling of entanglement entropy, the other by an area law. Employing stabilizer states and Clifford random unitary gates, we numerically investigate square lattices of linear dimension up to L=48L=48L=48 for two distinct measurement protocols. For both protocols, we observe a transition point where the dominant contribution in the entanglement entropy displays multiplicative logarithmic violations to the area law. We obtain estimates of the correlation length critical exponent at the percent level; these estimates suggest universal behavior and are incompatible with the universality class of 3D percolation.
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We study the entanglement dynamics in a generic quantum automaton circuit subjected to projective measurements. We design an efficient algorithm which not only allows us to perform large-scale simulation for the R\'enyi entropy, but also provides a physical picture for the entanglement dynamics, which can be interpreted in terms of a classical bit-string model which belongs to the directed percolation universality class. We study the purification dynamics of a state formed by Einstein-Podolsky-Rosen pairs, and the growth of entanglement starting from a product state. In both cases, we verify numerically that the dynamics is in the universality class of classical directed percolation.
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