  We study transport through an interacting model system consisting of a
central correlated site coupled to finite bandwidth tight-binding leads, which
are considered as effectively noninteracting. Its nonequilibrium properties are
determined by real-time propagation of the Kadanoff-Baym equations after
applying a bias voltage to the system. The electronic interactions on the
central site are incorporated by means of self-energy approximations at
Hartree-Fock, second Born and GW level. We investigate the conditions under
which multiple steady-state solutions occur within different self-energy
approximations, and analyze in detail the nature of these states from an
analysis of their spectral functions. At the Hartree-Fock level at least two
stable steady-state solutions with different densities and currents can be
found. By applying a gate voltage-pulse at a given time we are able to switch
between these solutions. With the same parameters we find only one steady-state
solution when the self-consistent second Born and GW approximations are
considered. We therefore conclude that treatment of many-body interactions
beyond mean-field can destroy bistability and lead to qualitatively different
results as compared those at mean-field level.
