Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models

Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo (QMC) sampling suffers from the sign problem, e.g., when solving a multiorbital quantum impurity model. Recently, two approaches have been proposed for efficient numerical treatment of Feynman diagrams: Tensor Cross Interpolation (TCI) for replacing the stochastic sampling and the Quantics Tensor Train (QTT) representation for compressing space-time dependence. Combining these approaches, we find low-rank structures in weak-coupling Feynman diagrams for a multiorbital electron-phonon model and demonstrate their efficient numerical integrations with exponential resolution in time and exponential convergence of error with respect to computational cost.