格点上的模型分数量子霍尔态：精确母哈密顿量与实现途径
Model Fractional Quantum Hall States on Lattices: Exact Parent Hamiltonians and Routes to Realization
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中文总结 AI 辅助
本文构建了使格点采样连续LLL模型态为精确零模的母哈密顿量，发现短程密度相互作用稳定Laughlin态，双体在位排斥支持Moore-Read三重态，为实验实现FQH态提供理论框架。
中文摘要 AI 辅助
工程化量子平台的最新进展使得在$\ u=1/2$处实现玻色子Laughlin态成为可能，并将非阿贝尔拓扑相带入了实验可及的范围。一个核心的理论挑战是建立一个统一框架，将格点分数量子霍尔（FQH）模型态、精确母哈密顿量和实验上可实现的相互作用联系起来。我们系统地构造了厄米母哈密顿量，使得在格点上采样的连续最低朗道能级（LLL）模型态成为其精确零模。利用这些模型流形作为定量参考，我们发现，在所研究的通量密度下，在投影格点LLL内，短程密度相互作用在$\ u=1/3$和$1/4$处稳定了Laughlin基态流形，而双体在位排斥在$\ u=1$处支持Moore-Read三重态。全多带计算揭示了一个鲜明的对比：在所研究的环面上，Laughlin流形对带间混合保持鲁棒，而Moore-Read三重态的光谱隔离性变差，并最终在接近带间尺度处与竞争态发生能级交叉。我们的框架为利用格点模型态指导寻找实验上可实现的阿贝尔和非阿贝尔FQH态提供了理论基础。
英文摘要
Recent advances in engineered quantum platforms have enabled the realization of bosonic Laughlin states at $ν=1/2$ and brought non-Abelian topological phases within experimental reach. A central theoretical challenge is to develop a unified framework connecting lattice fractional quantum Hall (FQH) model states, exact parent Hamiltonians, and experimentally accessible interactions. We systematically construct Hermitian parent Hamiltonians for which continuum lowest Landau level (LLL) model states sampled on lattice sites are exact zero modes. Using these model manifolds as quantitative references, we find that, within the projected lattice LLL at the flux densities studied, short-range density interactions stabilize Laughlin ground-state manifolds at $ν=1/3$ and $1/4$, while two-body onsite repulsion supports a Moore--Read triplet at $ν=1$. Full multiband calculations reveal a sharp contrast: the Laughlin manifolds remain robust against interband mixing on the studied tori, whereas the Moore--Read triplet becomes less spectrally isolated and eventually undergoes a level crossing with competing states near the interband scale. Our framework provides a theoretical foundation for using lattice model states to guide the search for experimentally accessible Abelian and non-Abelian FQH states.
发表机构
- International Center for Quantum Materials, Peking University（北京大学量子材料中心）
- Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
机构由 AI 辅助整理，请以论文原文为准。
