格点量子色动力学谱学与矩阵元的块兰佐斯算法
Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements
AI总结：
本文将基于兰佐斯算法和Cullum-Willoughby检验的关联函数分析框架扩展到格点QCD多插值算子关联函数矩阵，提出块兰佐斯算法的斜向推广及检验重构，较GEVP方法收敛更快、误差可控，无需拟合并完成原理验证。
摘要：
近期研究基于兰佐斯算法和Cullum-Willoughby检验的伪特征值滤波，提出了一个分析关联函数的新框架，该框架具有改进的收敛性和信噪比特性，以及对激发态效应的严格量化。在此，我们通过构建块兰佐斯算法的斜向推广，以及对Cullum-Willoughby检验的新物理驱动重构（可直接推广到块兰佐斯），将此框架扩展到格点量子色动力学（QCD）中由多个插值算子构建的关联函数矩阵分析。所得块兰佐斯方法直接扩展了广义特征值问题（GEVP）方法，后者可视为应用单次块兰佐斯迭代。块兰佐斯相较于GEVP方法具有定性和定量优势，类似于兰佐斯相较于标准有效质量的优势，包括更快收敛到基态和激发态能量、可显式计算的双边误差界、外部流矩阵元的直接提取，以及渐近恒定的信噪比。无需拟合或统计推断。我们对无噪声模拟数据示例以及格点QCD中的2×2质子关联函数矩阵进行了原理验证计算。
英文摘要：
Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
