A generic quantum Monte Carlo approach for electronic correlations in out-of-equilibrium systems.

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 a
determinantal diagrammatic Quantum Monte Carlo in the real time Keldysh
formalism.

Such an algorithm was already designed by Profumo at al. (PRB, 91 245154 (2015))
and can compute perturbation series for single quantities after an arbitrary
long (real) time evolution . We improved it to compute an entire time-dependent
function in a single run. With a similar sampling method and computation
time, the new algorithm gather much more information and give access to
dynamical quantities directly in real frequencies.

The algorithm has been tested on the Anderson impurity model at equilibrium,
and applied to the same system driven out of equilibrium by a bias voltage. In
these systems, we obtained 10 orders of the Green's function
perturbation series. To reach the non-perturbative regime, we developed a
robust resummation scheme based on conformal transforms of the complex plane in
the perturbation parameter.