We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint.

翻译：我们提出了离散莱曼表示（DLR）在虚时与松原频率下对三点关联函数和顶点函数的推广。该表示形式表现为虚时中精心选取的指数函数的线性组合，以及松原频率中简单极点的乘积，这些极点在给定温度和能量截断下具有普适性。我们提出了一种系统算法来生成紧凑的采样网格，通过求解线性系统即可获得此类展开的系数。研究表明，该表示的显式形式可用于计算包含无穷级数和（如极化函数或自能）的图表达式，且具有可控的高阶精度。这一系列技术建立了一个框架，使得涉及三点对象的计算能够以显著降低的计算开销和内存占用得以稳健实现。