标题： 磁场诱导的李厄格格子能带变形：阿哈罗诺夫-玻姆禁闭与泽曼分裂 显示英文标题

标题： Magnetic Field Induced Band Deformation in a Lieb Lattice:Aharonov-Bohm Caging and Zeeman Splitting

摘要： 平坦带系统对外部扰动非常敏感，为研究非常规局域化、输运和自旋物理提供了一条途径。 Lieb晶格是一种具有固有平坦带的二维几何结构，体现了这种行为，并可在超冷原子、光子阵列和超导电路中实验实现。 在本工作中，我们通过联合考虑轨道Peierls相位和Zeeman自旋分裂，对Lieb晶格中磁场引起的能带变形进行了全面研究。 垂直磁场产生Aharonov-Bohm囚禁，将粒子限制在局域化的平坦带态中，而Zeeman耦合则打破自旋简并并引起自旋分辨的能量偏移。 这两种机制之间的竞争导致丰富的能带重构和可调的自旋选择性平坦带现象。 这些结果确立了Lieb晶格作为合成量子平台（如超冷原子、光子晶格和超导电路）中自旋选择性输运和磁场工程的可控设置，为量子模拟及相关实验提供了指导原则，为在合成量子物质中受控工程自旋分辨局域化和平坦带物理开辟了道路。 显示英文摘要

摘要： Flat-band systems are highly sensitive to external perturbations, providing a route to study unconventional localization, transport, and spin physics. Lieb lattice, a two-dimensional geometry with an inherent flat band, exemplifies this behavior and is experimentally realizable in ultracold atoms, photonic arrays, and superconducting circuits. In this work, we present a comprehensive study of magnetic field induced band deformation in the Lieb lattice by jointly considering orbital Peierls phases and Zeeman spin splitting. A perpendicular magnetic flux generates Aharonov Bohm caging, confining particles into localized flat-band states, while Zeeman coupling lifts spin degeneracy and induces spin-resolved energy shifts. The competition between these two mechanisms gives rise to rich band restructuring and tunable spin-selective flat-band phenomena. These results establish the Lieb lattice as a controllable setting for spin-selective transport and magneticfield engineering in synthetic quantum platforms such as ultracold atoms, photonic lattices, and superconducting circuits, offering guiding principles for quantum simulation and the corresponding experiments, which opens the avenue for controlled engineering of spin-resolved localization and flat-band physics in synthetic quantum matter.