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We present a deterministic algorithm for the efficient evaluation ofimaginary time diagrams based on the recently introduced discrete Lehmannrepresentation (DLR) of imaginary time Green's functions. In addition to theefficient discretization of diagrammatic integrals afforded by itsapproximation properties, the DLR basis is separable in imaginary time,allowing us to decompose diagrams into linear combinations of nested sequencesof one-dimensional products and convolutions. Focusing on the strong couplingbold-line expansion of generalized Anderson impurity models, we show that ourstrategy reduces the computational complexity of evaluating an $M$th-orderdiagram at inverse temperature $\beta$ and spectral width $\omega_{\max}$ from$\mathcal{O}((\beta \omega_{\max})^{2M-1})$ for a direct quadrature to$\mathcal{O}(M (\log (\beta \omega_{\max}))^{M+1})$, with controllablehigh-order accuracy. We benchmark our algorithm using third-order expansionsfor multi-band impurity problems with off-diagonal hybridization and spin-orbitcoupling, presenting comparisons with exact diagonalization and quantum MonteCarlo approaches. In particular, we perform a self-consistent dynamicalmean-field theory calculation for a three-band Hubbard model with strongspin-orbit coupling representing a minimal model of Ca$_2$RuO$_4$,demonstrating the promise of the method for modeling realistic stronglycorrelated multi-band materials. For both strong and weak coupling expansionsof low and intermediate order, in which diagrams can be enumerated, our methodprovides an efficient, straightforward, and robust black-box evaluationprocedure. In this sense, it fills a gap between diagrammatic approximations ofthe lowest order, which are simple and inexpensive but inaccurate, and thosebased on Monte Carlo sampling of high-order diagrams.

Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion