Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits

Abstract

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 $\sqrt{t\ln t}$, saturating the bound established by Huang [IOP SciNotes 1, 035205 (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.

17 pages, 14 figures

References in corpus (5)

• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Measurement-induced phase transitions in quantum automaton circuits
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Measurement-induced criticality in ${\mathbb{Z}}_2$-symmetric quantum automaton circuits
• Entanglement structure in the volume-law phase of hybrid quantum automaton circuits

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• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport