The evaluation of Feynman diagrams is a fundamental computational task, and bottleneck, in Green's function methods for quantum many-body calculations. In that setting, diagrammatic expressions typically take the form of high-dimensional integrals involving products of matrix-valued functions of a single time variable. The leading diagram evaluation methods are based on Monte Carlo or quasi-Monte Carlo sampling which, despite widespread success, suffer from low numerical accuracy, poor computational scaling at low temperatures, and lack of robustness due to the numerical sign problem. I will describe a fast, deterministic algorithm to evaluate diagrams of low-to-intermediate order with controllable, high-order accuracy. The central idea is to expand certain factors in the integrand as sums of exponentials using rational approximation techniques, and then use separation of variables to decompose the multiple integrals into sequences of nested convolutions. We apply this idea to the bold hybridization expansion of a quantum impurity model, obtaining a fast, approximate solver for quantum embedding methods via dynamical mean-field theory.
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