Reconstructing Nonequilibrium Regimes of Quantum Many-Body Systems from the Analytical Structure of Perturbative Expansions

We propose a systematic approach to the nonequilibrium dynamics of strongly interacting many-body quantum systems, building upon the standard perturbative expansion in the Coulomb interaction. High-order series are derived from the Keldysh version of the determinantal diagrammatic quantum Monte Carlo algorithm, and the reconstruction beyond the weak-coupling regime of physical quantities is obtained by considering them as analytic functions of a complex-valued interaction U . Our advances rely on two crucial ingredients: (i) a conformal change of variable, based on the approximate location of the singularities of these functions in the complex U plane, and (ii) a Bayesian inference technique, that takes into account additional known nonperturbative relations, in order to control the amplification of noise occurring at large U . This general methodology is applied to the strongly correlated Anderson quantum impurity model and is thoroughly tested both in and out of equilibrium. In the situation of a finite voltage bias, our method is able to extend previous studies, by bridging with the regime of unitary conductance and by dealing with energy offsets from particle-hole symmetry. We also confirm the existence of a voltage splitting of the impurity density of states and find that it is tied to a nontrivial behavior of the nonequilibrium distribution function. Beyond impurity problems, our approach could be directly applied to Hubbard-like models, as well as other types of expansions.