Floquet $\mathbb{Z}_N$ 拓扑序中的手性 Parafermion
Chiral Parafermions in Floquet $\mathbb{Z}_N$ Topological Order
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中文总结 AI 辅助
该研究在广义 Kitaev 蜂窝模型中实现 $\mathbb{Z}_N$ Floquet 拓扑序，揭示手性 parafermion 边缘模式及任意子动力学嬗变，为量子处理器探索非平衡拓扑现象提供平台。
中文摘要 AI 辅助
Floquet 拓扑序 (FTO) 将拓扑性质拓展到平衡态之外，产生了诸如任意子动力学嬗变等现象。在此，我们利用三步周期驱动，在具有时钟自由度的广义 Kitaev 蜂窝模型中实现了 $\mathbb{Z}_N$ FTO。该驱动系统允许一种涌现描述，即受约束的 parafermion 与守恒的 $\mathbb{Z}_N$ 规范场耦合。在边界处，驱动产生了手性 parafermionic Floquet 边缘模式。我们通过关联函数解析了它们的传播，通过激进的手性幺正指标刻画了它们的分数化量子信息输运，并利用它们的动力学探测交换统计。在体态中，我们利用非平衡环序参量探索了动力学任意子嬗变。在 Floquet 甜点（驱动变为 Clifford 型）处，这些现象可通过 stabilizer 模拟访问。远离该点的短时矩阵乘积态模拟表明，手性边缘响应在可访问时间内持续存在。我们的结果确立了 $\mathbb{Z}_N$ Kitaev 模型作为在基于 qudit 的量子处理器上探索本质非平衡拓扑现象的平台。
英文摘要
Floquet topological order (FTO) extends topology beyond equilibrium, giving rise to phenomena, such as the dynamical transmutation of anyons. Here, we realize $\mathbb{Z}_N$ FTO in a generalized Kitaev honeycomb model with clock degrees of freedom using a three-step periodic drive. The driven system admits an emergent description in terms of constrained parafermions coupled to conserved $\mathbb{Z}_N$ gauge fields. At the boundary, the drive generates chiral parafermionic Floquet edge modes. We resolve their propagation through correlation functions, characterize their fractional quantum-information transport through the radical chiral unitary index, and use their dynamics to probe exchange statistics. In the bulk, we explore the dynamical anyon transmutation with a non-equilibrium loop order parameter. At a Floquet sweet spot, where the drive becomes Clifford, these phenomena can be accessed using stabilizer simulations. Short-time matrix-product-state simulations away from this point show that the chiral edge response persists at accessible times. Our results establish $\mathbb{Z}_N$ Kitaev models as a setting for exploring intrinsically non-equilibrium topological phenomena on qudit-based quantum processors.
发表机构
- Technical University of Munich（慕尼黑工业大学）
- Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
- Harvard University（哈佛大学）
- University of Nottingham（诺丁汉大学）
机构由 AI 辅助整理，请以论文原文为准。
