发表机构
University of California, Los Angeles（加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种混合确定性-随机方法，在实空间中高效构造库仑算子，结合低秩近似与随机探测，在扩展哈伯德模型中验证精度并显著降低计算成本。
AI 中文摘要
我们提出了一种高效的混合确定性-随机方法，用于在实空间中构造库仑算子，该方法在全频谱范围内保持精度。相互作用的主要长程分量通过紧凑的低秩近似以确定性方式捕获，该近似使用切比雪夫滤波子空间迭代构建，而剩余的频谱尾部则使用少量随机向量进行无偏探测。所得算子被用于周期、扰动和非周期三维晶格上的扩展哈伯德哈密顿量的自洽场计算中进行基准测试。我们通过实施刀切校正来考虑可观测量中的随机偏差。该方法随着确定性秩和随机样本数量的增加而系统性地改进，同时大幅降低了构造库仑矩阵的计算成本。
英文摘要
We present an efficient mixed deterministic-stochastic approach for constructing the Coulomb operator in real space that preserves accuracy across the full spectral range. The dominant long-range components of the interaction are captured deterministically via a compact, low-rank approximation, constructed using Chebyshev-filtered subspace iteration, while the remaining spectral tail is treated using unbiased probing with a small number of stochastic vectors. The resulting operator is benchmarked within self-consistent field calculations for the extended Hubbard Hamiltonian on periodic, perturbed, and non-periodic three-dimensional lattices. We account for stochastic bias in observables by implementing a jackknife correction. The method systematically improves with deterministic rank and stochastic sample count, while substantially reducing the computational cost of constructing the Coulomb matrix.
Comments14 pages, 5 figures
