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arXiv:2002.12372 · Physical Review Letters

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

Marjan Maček, Philipp T. Dumitrescu, Corentin Bertrand, Bill Triggs, Olivier Parcollet, Xavier Waintal

Published Jul 22, 2020• 47 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.125.047702

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We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the M\o{}ller-Plesset (MPn\mathrm{MP}nMPn) perturbation series, obtaining accurate correlation energies up to n=5n=5n=5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.
We use tensor network techniques to obtain high-order perturbative diagrammatic expansions for the quantum many-body problem at very high precision.The approach is based on a tensor train parsimonious representation of the sum of all Feynman diagrams, obtained in a controlled and accurate way with the tensor cross interpolation algorithm.It yields the full time evolution of physical quantities in the presence of any arbitrary time-dependent interaction.Our benchmarks on the Anderson quantum impurity problem, within the real-time nonequilibrium Schwinger-Keldysh formalism, demonstrate that this technique supersedes diagrammatic quantum Monte Carlo by orders of magnitude in precision and speed, with convergence rates 1=N 2 or faster, where N is the number of function evaluations.The method also works in parameter regimes characterized by strongly oscillatory integrals in high dimension, which suffer from a catastrophic sign problem in quantum Monte Carlo calculations.Finally, we also present two exploratory studies showing that the technique generalizes to more complex situations: a double quantum dot and a single impurity embedded in a two-dimensional lattice.