标题： 相空间方法在正方形-八边形格点中的Wannier配对和Bogoliubov轨道研究 显示英文标题

标题： Phase-Space Approach to Wannier Pairing and Bogoliubov Orbitals in Square-Octagon Lattices

摘要： 低能晶格模型是研究多体物理和系统与测量场之间相互作用的基础。 一个关键挑战是识别适当的准粒子态，这些态在动量空间和实空间之间规范变换的同时保留关联性、纠缠性和几何性质——通常称为Wannier阻抗。 在这里，我们引入了一种相空间方法来绕过这些阻抗。 我们不是将相空间视为流形，而是通过每个动量处的布洛赫向量空间嵌入实空间。 轨道和自旋态通过布洛赫向量的乘积态引入，而量子统计、关联性、拓扑结构和纠缠性则从哈密顿量继承而来。 我们将此框架应用于探索相空间中非常规配对对称性和Bogoliubov-de Gennes (BdG) 方程。 我们的发现表明，尽管超导性表现出全局相干性，但局域Wannier轨道对称性主要决定了配对对称性。 我们通过构建具有人工规范场的平带，在相空间中解析地求解了由自旋涨落介导的配对对称性。 我们使用密度泛函理论（DFT）验证了平方八边形超导体Lu$_2$Fe$_3$Si$_5$的模型，揭示了无节点$s^{\pm}$和有节点$s_{z^2}$配对对称性的共存。 这一相空间框架为复杂多体系统及其奇异激发提供了一个稳健且无阻抗的晶格模型。 显示英文摘要

摘要： Low-energy lattice models are the cornerstone for studying many-body physics and interactions between the system and measurement fields. A key challenge is identifying appropriate quasiparticle states that canonically transform between momentum and real space while retaining the correlation, entanglement, and geometric properties - generally called the Wannier obstruction. Here, we introduce a phase-space approach to bypass these obstructions. Instead of treating the phase space as a manifold, we embed a real space through a Bloch vector space at each momentum. Orbital and spin states are introduced through product states with the Bloch vector, while quantum statistics, correlations, topology, and entanglements are inherited from the Hamiltonian. We apply this framework to explore the unconventional pairing symmetry and the Bogoliubov-de Gennes (BdG) equation in phase space. Our findings demonstrate that while superconductivity exhibits global coherence, the local Wannier orbital symmetry primarily determines the pairing symmetry. We analytically solve the spin-fluctuation-mediated pairing symmetry on the phase space by engineering a flat band with artificial gauge fields. We validate the model on the square-octagon superconductor Lu$_2$Fe$_3$Si$_5$ using density functional theory (DFT), revealing the coexistence of nodeless $s^{\pm}$ and nodal $s_{z^2}$ pairing symmetries. This phase-space framework provides a robust, obstruction-free lattice model for complex many-body systems and their exotic excitations.