  Employing a combination of a sign-free Monte Carlo approach and
nonequilibrium Green's function techniques, we study nonequilibrium charge
transport in a model heterostructure, where a two-dimensional spin-less
Falicov-Kimball system is coupled to two noninteracting leads. We show that the
transport characteristic depends sensitively on the electrostatic potential in
the system and exhibits different properties for different phases of the
Falicov-Kimball model. In particular, pronounced step-like changes of the
current and transmission are observed at the phase boundaries, evident even on
a logarithmic scale. Analyzing finite size effects, we find that with the
method used a relatively small system can be utilized to address specific
thermodynamic limits.
