Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime

We present a general-purpose algorithm to extrapolate a low-rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum many-body perturbative expansions in the real-time Keldysh formalism, considered as a function of time $t$ and interaction $U$. These functions are of remarkably low rank. This property, combined with the convergence of the perturbative expansion in $U$ both at finite $t$ (for any $U$), and small $U$ (for any $t$), is sufficient for our algorithm to reconstruct the physical quantity at long time, strong coupling regime. Our method constitutes an alternative to standard resummation techniques in perturbative methods, such as diagrammatic quantum Monte Carlo. We benchmark it on the single impurity Anderson model and show that it is successful even in some regime where standard conformal mapping resummation techniques fail.