Fast evaluation of imaginary-time Feynman diagrams via sum-of-exponentials expansions

We present a deterministic algorithm for the efficient evaluation of low-to-intermediate-order imaginary time Feynman diagrams appearing in the bold strong coupling expansion of a quantum impurity model. M-th order diagrams can be evaluated using sum-of-exponentials expansions produced by the discrete Lehmann representation of imaginary time Green’s functions, and separation of variables. This reduces the computational complexity of evaluating an M-th order diagram at inverse temperature β from O(β^2M−1) for a scheme based on direct quadrature to O(M log^M+1 β). We show that the computational cost can be further reduced by a matrix-based hybridization decomposition, and efficient pole-fitting of the Green's function. Our method provides an efficient, straightforward, and robust black-box evaluation procedure, leading to a new impurity solver for dynamical mean-field theory calculations which goes beyond the lowest-order diagrammatic approximations while avoiding the slow convergence and sign problem of Monte Carlo-based schemes.