标题： 合成费米-哈伯德双层中的新兴基矢材料 显示英文标题

标题： Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers

摘要： 我们研究了在人工费米-哈伯德双层晶格中出现的键向性自旋-自旋相互作用，这种晶格可以通过超冷费米子在拉曼光晶格中实现。 该模型利用人工维度通过拉曼辅助隧穿耦合两个蜂窝状层，每个层对应于不同的超精细原子态，并且还通过冷原子散射引起的层间哈伯德排斥来耦合。在半满填充的强耦合极限下，我们推导出有效自旋哈密顿量，其中包括基特维（Kitaev）、海森堡、非对角交换（$\Gamma$-耦合）以及可调Dzyaloshinskii-Moriya相互作用。 我们确定了特定的构型，这些构型在与基特维材料相关的各种扰动下生成铁磁性和反铁磁性的基特维耦合，提供了一个可调节平台，可以探索量子自旋液体如何从迁移费米子系统中产生。 我们分析了费米液体和莫特绝缘体相，突出显示了狄拉克准粒子和马约拉纳准粒子之间的对应关系，以及可能的相变。 在极端各向异性极限下，我们证明该模型简化为准一维梯子中的层间带状结构，允许使用矩阵乘积态对相关基态进行数值研究。 我们发现从对称保护拓扑绝缘体到基特维类似区域的转变，该区域以非局域弦序为特征。 我们的研究表明，基于拉曼光晶格的冷原子量子模拟器可以成为扩展基特维模型的实验场，连接迁移费米子系统和自旋液体物理。 显示英文摘要

摘要： We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ($\Gamma$-couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.