Discrete Lehmann representation of three-point functions

We present a method of compactly representing three-point correlation and vertex functions in imaginary time and Matsubara frequency. This is a generalization of the discrete Lehmann representation (DLR) of the single-particle imaginary time Green's function, and takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency. These basis functions are universal for a given temperature and energy cutoff, and their number scales mildly with both quantities. We present a systematic algorithm to generate compact sampling grids from which the coefficients of such an expansion can be obtained, and show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums 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.