Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/N^1/2 in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.
Finally, I will also present a recent extension of the technique to compute whole time-dependent Green functions via a kernel approach.