Physical Review X (Nov 2022)

Learning Feynman Diagrams with Tensor Trains

  • Yuriel Núñez Fernández,
  • Matthieu Jeannin,
  • Philipp T. Dumitrescu,
  • Thomas Kloss,
  • Jason Kaye,
  • Olivier Parcollet,
  • Xavier Waintal

Journal volume & issue
Vol. 12, no. 4
p. 041018


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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.