Variational cluster approach for correlated many-body systems out of equilibrium

We present a
numerical approach that allows to compute
steady state properties of strongly correlated quantum many-body
systems out of equilibrium [1].
The method
is based on a combination of
variational cluster approach
with the nonequilibrium Green's function (Keldysh) formalism.

We apply the method to non-linear transport
across a strongly correlated quantum wire
described by the fermionic Hubbard model, and across a correlated
quantum dot [2].
In the last case, we benchmark
results for the steady-state current
with data from
Matrix Product State based time
evolution.
We show that for low to medium interaction strength,
a simple cluster perturbative approach
already yields good
results, while for larger interaction strength the
self-consistent
feedback provided by the variational condition
significantly enhances the accuracy.
Finally, we illustrate how the method bridges to nonequilibrium
cluster dynamical mean-field theory.