Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions
Marjan Maček, Philipp T. Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, Xavier Waintal
Abstract
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/sqrt[N] in Monte Carlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.
Topics & Concepts
Quantum Monte CarloMonte Carlo methodScalingPerturbation theory (quantum mechanics)Statistical physicsPhysicsQuantumDiagrammatic reasoningMonte Carlo integrationMonte Carlo molecular modelingQuantum mechanicsComputer scienceMathematicsMarkov chain Monte CarloStatisticsProgramming languageGeometryAdvanced Chemical Physics StudiesTheoretical and Computational PhysicsQuantum and electron transport phenomena