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：本文提出了离散Lehmann表示（DLR）在虚时与松原频率下三点关联函数及顶点函数上的推广。该表示形式为一系列精心选取的虚时指数函数的线性组合，以及松原频率中单极点乘积的线性组合，这些基函数对于给定温度与能量截断具有普适性。我们提出了一种系统化算法来生成紧凑的采样网格，通过求解线性方程组即可获得此类展开的系数。我们证明了该表示的显式形式可用于计算涉及无穷松原求和的图表达式（如极化函数或自能函数），并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方法能够以显著降低的计算成本与内存占用量稳健地实现。