标题： 使用传递矩阵形式从格点QCD关联函数中估算能级 显示英文标题

标题： Estimating energy levels from lattice QCD correlation functions using a transfer matrix formalism

摘要： 我们提出了一种高效的方法，通过计算与格点QCD哈密顿量相关的转移矩阵的特征值，从格点QCD关联函数中提取能级。 虽然在数学和数值上等价于最近引入的Lanczos过程，但我们的方法引入了一种使用核密度估计器（KDE）和高斯卷积直方图方法的新颖方案来去除虚假特征值。 这种策略能够得出稳健且稳定的能量谱估计，其效率优于Cullum-Willoughby滤波技术。 此外，我们详细说明了如何应用该方法从两点关联函数中提取重叠因子，以及从带有电流插入的三点函数中提取矩阵元。 此外，我们将该方法扩展到适应由变分基算符构建的相关矩阵，并采用其块形式。 我们通过计算多种强子（包括几个核子）的两个最低能级来展示该框架的有效性。 尽管信噪比没有显著提高，但提取的能级被发现比传统技术获得的更可靠。 在给定的统计系综内，所提出的方法能够有效捕捉统计不确定性和系统误差，包括来自拟合窗口选择的误差，使其成为格点QCD分析的稳健且实用的工具。 显示英文摘要

摘要： We present an efficient method for extracting energy levels from lattice QCD correlation functions by computing the eigenvalues of the transfer matrix associated with the lattice QCD Hamiltonian. While mathematically and numerically equivalent to the recently introduced Lanczos procedure, our approach introduces a novel prescription for removing spurious eigenvalues using a kernel density estimator (KDE) and Gaussian-convoluted histogram method. This strategy yields a robust and stable estimate of the energy spectrum, outperforming the Cullum-Willoughby filtering technique in efficiency. In addition, we detail how this method can be applied to extract overlap factors from two-point correlation functions, as well as matrix elements from three-point functions with a current insertion. Furthermore, we extend the methodology to accommodate correlation matrices constructed from a variational basis of operators, with its Block formulation. We demonstrate the efficacy of this framework by computing the two lowest energy levels for a broad range of hadrons, including several nuclei. Although the signal-to-noise ratio is not significantly improved, the extracted energy levels are found to be more reliable than those obtained with conventional techniques. Within a given statistical ensemble, the proposed method effectively captures both statistical uncertainties and systematic errors, including those arising from the choice of fitting window, making it a robust and practical tool for lattice QCD analysis.