发表机构
Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University; Wuhan Institute of Quantum Technology; School of Artificial Intelligence, Wuhan University（教育部人工微纳结构重点实验室和武汉大学物理科学与技术学院; 武汉量子技术研究院; 武汉大学人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出分层傅里叶相位投影（HPP）方法，通过可复用的空间层级逐步消除混叠并利用密度矩阵局域性，实现大规模电子结构计算中局部可观测量的高效、可控收敛计算，兼顾精度与计算成本。
AI 中文摘要
大规模电子结构计算需要在不显式构造所有占据轨道的情况下高效访问局部可观测量。我们开发了分层傅里叶相位投影（HPP），该方法将傅里叶探针组织成可复用的空间层级，在利用密度矩阵局域性的同时逐步消除短程混叠。该方法提供了从低成本局部估计到所选数值占据算符的投影精确极限的系统性细化，且不丢弃先前评估的响应。使用半导体和金属体系的冻结Kohn-Sham哈密顿量进行的测试表明，电子密度和非局域赝势力的收敛具有可控性，固定局部精度所需的探测分辨率对尺寸依赖性较弱，且在固定探测工作量下直接计算成本呈近线性增长。层级间的变化进一步为在有限精度下终止细化提供了实用信息。HPP将电子局域性、可观测量精度和计算工作量统一在单一分层框架内，为大规模电子结构计算中的局部量提供了一条可扩展的途径。
英文摘要
Large-scale electronic-structure calculations require efficient access to local observables without explicitly constructing all occupied orbitals. We develop hierarchical Fourier phase projection (HPP), which organizes Fourier probes into a reusable spatial hierarchy that progressively removes short-range aliasing while exploiting density-matrix locality. The method provides systematic refinement from low-cost local estimates to the projection-exact limit of the chosen numerical occupation operator, without discarding previously evaluated responses. Tests using frozen Kohn--Sham Hamiltonians for semiconducting and metallic systems demonstrate controllable convergence of electron densities and nonlocal pseudopotential forces, weak size dependence of the probing resolution required for a fixed local accuracy, and near-linear growth of the direct computational cost at fixed probing workload. Inter-level changes further provide practical information for terminating the refinement at finite accuracy. HPP connects electronic locality, observable accuracy, and computational effort within a single hierarchical framework, providing a scalable route to local quantities in large-scale electronic-structure calculations.
Comments14 pages, 7 figures
