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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 , 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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Chiral spin liquid in a Z_3 Kitaev model
We study a Z_3 Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible U(1)_{12} chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped two-dimensional bulk. The topological entanglement entropy is extracted and found to be in agreement with the U(1)_{12} topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the U(1)_{12} topological phase. We conclude by discussing several open questions.
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- Award ID(s):
- 1846109
- PAR ID:
- 10505737
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 109
- Issue:
- 15
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevB.109.155161
