# Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions

## TL;DR

This paper introduces a novel method combining conformal mapping and Bayesian inference to reconstruct non-equilibrium dynamics of strongly interacting quantum systems from perturbative series, extending analysis beyond weak coupling regimes.

## Contribution

The authors develop a systematic approach that reconstructs non-equilibrium quantum many-body dynamics from high-order perturbative expansions using complex analysis and Bayesian inference, applicable to strongly correlated systems.

## Key findings

- Extended analysis of Anderson impurity model under bias.
- Confirmed voltage splitting of impurity density of states.
- Bridged the gap to the unitary conductance regime.

## Abstract

We propose a systematic approach to the non-equilibrium 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 determinantal diagrammatic Quantum Monte Carlo, 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; ii) a Bayesian inference technique, that takes into account additional known non-perturbative 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 non-trivial behavior of the non-equilibrium distribution function. Beyond impurity problems, our approach could be directly applied to Hubbard-like models, as well as other types of expansions.