Enhancing Diagrammatic quantum Monte Carlo sampling through Normalizing Flows

Diagrammatic quantum Monte Carlo (DMC) is a powerful numerical method able to obtain approximation-free estimates of diagrammatic perturbative expansions. The potential of obtaining exact estimates of quasi-particle energies and thermodynamic observables makes DMC a wildly studied tool with applications in different fields of condensed matter. However, all today applications remains limited to the study of effective Hamiltonians models due to DMC developing critical slowing down effects as one approaches real materials. Other Monte Carlo methods address such problem using global updates strategies that are not suited for the DMC framework. Normalizing Flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in DMC, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams as an effective global update. The resulting NF-augmented DMC is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in DMC.