Learning Feynman Diagrams with Tensor Trains

• DOI: 10.48550/arxiv.2207.06135
• Publication Date: 2022-01-01
• Authors: Y. Núñez-Fernández; Matthieu Jeannin; Philipp T. Dumitr...; Thomas Kloss; Jason P. Kaye; Olivier Parcollet; Xavier Waintal
• Keywords: Diagrammatic reasoning

We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very precision. The approach is based on a train parsimonious representation of sum all Feynman diagrams, obtained in controlled and accurate way with cross interpolation algorithm. It yields full time evolution physical quantities presence any arbitrary dependent interaction. Our benchmarks Anderson impurity problem, within real non-equilibrium Schwinger-Keldysh formalism, demonstrate that this technique supersedes Quantum Monte Carlo by orders magnitude precision speed, convergence rates $1/N^2$ or faster, where N number function evaluations. method also works parameter regimes characterized strongly oscillatory integrals dimension, which suffer from catastrophic sign Monte-Carlo. Finally, we present two exploratory studies showing generalizes more complex situations: double dot single embedded dimensional lattice.