Block-sparse evaluation of imaginary-time strong-coupling Feynman diagrams

We present an algorithm for the evaluation of imaginary-time Feynman diagrams in the strong-coupling expansion of the Anderson impurity model that makes use of sparse linear algebra to accelerate existing deterministic methods. A symmetry in an impurity model implies the existence of a Fock space basis in which imaginary-time Green's function and pseudoparticle field operators have similar block structures. This enables efficient multiplications and convolutions of matrix-valued functions when evaluating diagrammatic expansions. We show that when used in tandem with other techniques, like the use of sum-of-exponentials approximations for the impurity-bath hybridization and Green's functions, this algorithm achieves a tangible improvement in computational complexity with respect to the number of orbitals, n. For instance, we observe an O(n) speedup in problems with at least total particle-number symmetry. This fast impurity solver raises the possibility of performing heretofore infeasable calculations on dynamical mean-field theory models with larger numbers of orbitals.