标题： 拓扑铁磁相互作用在Lieb晶格中通过弱相互作用交织 显示英文标题

标题： Topology-ferrimagnetism intertwining via weak interactions in Lieb lattices

摘要： 关于量子多体系统的常见观点是，涌现的相通常属于朗道-金兹堡范式或拓扑分类。 实验实现自发对称性破缺和拓扑序的交织涌现仍然具有挑战性。 在此，我们提出一个实验上可访问的平台，用于研究自旋轨道耦合的Lieb晶格中的磁性拓扑态。 值得注意的是，我们在多体基态中观察到拓扑特性（由陈数和Bott指标量化）与自发对称性破缺序（如亚铁磁性）的共存。 结合动力学平均场理论和Hartree-Fock近似的计算分析揭示了一个显著的参数区域，在该区域中即使在弱相互作用下也会出现磁性拓扑绝缘体。 这种非传统的现象源于Lieb晶格独特的能带结构，该结构促进了由相互作用驱动的对称性破缺与自旋轨道耦合引起的能带反转之间的协同作用。 关键的是，由于自旋极化和自旋缠绕源自相同的相互作用、自旋态原子，它们作为本质上耦合的现象同时出现。 我们进一步提出了一种针对超冷原子的具体实验实施方案，利用目前可用的拉曼晶格技术。 我们的发现为探索强关联系统中对称性破缺态与拓扑序之间的相互作用铺平了道路。 显示英文摘要

摘要： A common wisdom about quantum many-body systems is that emergent phases typically fall into either the Landau-Ginzburg paradigm or topological classifications. Experimentally realizing the intertwined emergence of spontaneous symmetry breaking and topological order remains challenging. Here, we present an experimentally accessible platform for studying magnetic topological states in a spin-orbit-coupled Lieb lattice. Remarkably, we observe the coexistence of topological characteristics, quantified by the Chern number and Bott index, with spontaneous symmetry-breaking orders, such as ferrimagnetism, in the many-body ground states. Computational analyses combining dynamical mean-field theory and Hartree-Fock approximations reveal a pronounced parameter regime where magnetic topological insulators emerge even under weak interactions. This unconventional phenomenon originates from the Lieb lattice's unique band structure, which facilitates the synergy between interaction-driven symmetry breaking and spin-orbit coupling induced band inversion. Crucially, spin polarization and spin winding co-emerge as inherently coupled phenomena due to their shared origin in the same interacting, spinful atoms. We further propose a specific experimental implementation scheme for ultracold atoms, utilizing currently available Raman lattice techniques. Our findings pave the way for exploring the interplay between symmetry-broken states and topological order in strongly correlated systems.