AI 中文总结
该研究提出单元胞自然轨道（CNOs）方法，以构建能捕捉量子材料目标带几何与电荷密度的局域基，并将其应用于扭转双层WSe₂的晶格模型构建。
AI 中文摘要
理解关联量子物质需从低能相互作用的单粒子态的精确模型入手，这些态涉及色散、带几何、轨道内容与电荷密度。在诸多情形中，尤其是莫尔材料的拓扑能带，很难找到用少量局域轨道实现此目的的实空间描述。本文提供了一种系统方法，用于识别能最佳捕捉任意选定能带集的带几何与电荷密度的局域自由度。我们使用单元胞单粒子约化密度矩阵（UC-1pRDM），其通过将目标能带的投影器限制于单个单元胞得到。该矩阵的本征态被称为单元胞自然轨道（CNOs），它们构成了由布洛赫波函数与实空间划分选择唯一确定的局域、对称基。其本征值衡量每个CNO在目标能带中的占据情况，量化单元胞边界间的纠缠以及多轨道特性的重要性。一组能最大化总谱权重并重现目标带对称性的CNOs，为Wannier化提供了最优试探态。我们通过构建扭转双层WSe₂的晶格模型来例证此方法，该模型可追踪不同扭转角下的轨道内容。
英文摘要
Understanding correlated quantum matter starts with an accurate model of the single-particle states that interact at low energies: their dispersion, band geometry, orbital content and charge density. In many cases, notably the topological bands of moire materials, it is not straightforward to find a real-space description with a few local orbitals that accomplishes this task. Here we provide a systematic way to identify the local degrees of freedom that best capture the band geometry and charge density of any chosen set of bands. We use the unit-cell one-particle reduced density matrix (UC-1pRDM), obtained by restricting the projector onto the target bands to a single unit cell. Its eigenstates, which we call cell natural orbitals (CNOs), form a local, symmetric basis uniquely determined by the Bloch wavefunctions and the choice of real-space partition. Their eigenvalues measure the occupation of each CNO in the target bands, quantifying entanglement across unit-cell boundaries and the importance of multi-orbital character. A set of CNOs that maximizes total spectral weight and reproduces the target band symmetries provides optimal trial states for Wannierization. We exemplify this by constructing a lattice model for twisted bilayer WSe$_2$ that tracks the orbital content across twist angles.
Comments17 pages, 7 figures
