Nonequilibrium steady-state density of states for a strongly correlated electron system in the presence of a large electric field.

The electronic density of states (DOS) of the Falicov-Kimball model in a constant uniform electric field $E$ is calculated using a Kadanoff-Baym-Keldysh nonequilibrium Green's function technique and dynamical mean-field theory. When the electron-electron interaction $U$ vanishes, the DOS is the Wannier-Stark ladder of delta functions spaced by the Bloch frequency. If $U$ is increased, the delta function peaks initially broaden due to the scattering, but ultimately evolve into a continuous structure for large $U$'s. As $E$ is increased from small values, where linear response theory can be used and we see broadened Wannier-Stark peaks, the DOS develops a shape with large peaks at miniband edges, separated in energy by $U$. We verify the accuracy of our calculations by checking the DOS against frequency-moment sum rules, and an independent transient-response calculation of the Green's functions at long times. While our formalism has been applied to the Falicov-Kimball model, it can also be directly extended to other models like the Hubbard or periodic Anderson model, by using more complicated impurity problem solvers.