Discrete Lehmann representation of three-point functions
<|reference_start|>Discrete Lehmann representation of three-point functions: 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.<|reference_end|>
@article{kiese2024discrete,
    title={Discrete Lehmann representation of three-point functions},
    author={Dominik Kiese and Hugo U. R. Strand and Kun Chen and Nils Wentzell and
  Olivier Parcollet and Jason Kaye},
    journal={arXiv preprint arXiv:2405.06716},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06716},
    primaryClass={physics.comp-ph cond-mat.str-el cs.NA math.NA}
}