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

Marjan Maček (1) , Philipp Dumitrescu (2) , Corentin Bertrand (2) , Bill Triggs (3) , Olivier Parcollet (2, 4) , Xavier Waintal (5)

1 GT - Laboratory of Quantum Theory
2 Flatiron Institute
3 DAO - Données, Apprentissage et Optimisation
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681
5 PHELIQS - PHotonique, ELectronique et Ingénierie QuantiqueS

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. 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 in Monte Carlo. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.

Domaines: Matière Condensée [cond-mat]; Physique Quantique [quant-ph]; Micro et nanotechnologies/Microélectronique; Machine Learning [stat.ML]

Marjan Maček, Philipp Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, et al.. Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions. Physical Review Letters, 2020, 125 (4), pp.047702. ⟨10.1103/PhysRevLett.125.047702⟩. ⟨hal-03044608⟩