标题： 量子材料的电子结构自助法 显示英文标题

标题： Bootstrapping the Electronic Structure of Quantum Materials

摘要： 过去几十年里，固态物理和材料科学领域在材料的理论建模方面取得了显著进展，但许多常用方法难以准确捕捉强电子关联。近年来，量子材料领域的广泛兴趣进一步突显了开发能够严谨处理这种关联的理论方法的需求——在这些材料中，强关联在决定其行为的量子效应中起着至关重要的作用。 在此，我们提出了一种变分双电子约化密度矩阵（2-RDM）理论的周期性推广，这是一种无需依赖波函数即可最小化基态能量的“自举型”方法。通过半定规划直接计算2-RDM，并结合$N$表示性条件，确保了对强关联电子系统的准确处理。利用平移对称性，我们大幅降低了计算复杂度，使该方法能够应用于实际材料规模的系统。 此外，我们引入了一种替代常规能带结构的方法：自然轨道占据数能带，由于不受平均场假设的影响，这种方法能够更深入地揭示电子关联效应。我们通过将此理论应用于氢链、二硫化钼和氧化镍，展示了自然轨道占据能带在密度泛函理论失效的区域中正确捕获电子特性。这项工作标志着在使用约化密度矩阵而非波函数描述量子材料电子结构方面迈出了重要一步。 显示英文摘要

摘要： The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong electron correlation accurately. Recent widespread interest in quantum materials -- where strong correlation plays a crucial role in the quantum effects governing their behavior -- further highlights the need for theoretical methods capable of rigorously treating such correlation. Here, we present a periodic generalization of variational two-electron reduced density matrix (2-RDM) theory, a bootstrapping-type method that minimizes the ground-state energy as a functional of the 2-RDM without relying on the wavefunction. The 2-RDM is computed directly by semidefinite programming with $N$-representability conditions, ensuring accurate treatment of strongly correlated electronic systems. By exploiting translational symmetry, we significantly reduce computational scaling, enabling applications to realistic materials-scale systems. Additionally, we introduce an alternative to conventional energy band structures: natural-orbital occupation-number bands, which, being independent of mean-field assumptions, offer deeper insights into electron correlation effects. We demonstrate the effectiveness of this approach by applying the theory to hydrogen chains, molybdenum disulfide, and nickel oxide, showing that natural-orbital occupation bands correctly capture electronic character in regimes where density functional theory fails. This work represents a major step toward accurately describing the electronic structure of quantum materials using reduced density matrices rather than wavefunctions.