Nonequilibrium Dynamical Mean-Field Theory: An Auxiliary Quantum Master Equation Approach

We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green’s function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.

Figure 1

Schematic representation of the system at study.

Figure 2

Imaginary part of the DMFT and effective bath hybridization functions [retarded ($R$) and Keldysh ($K$) components] for $\Phi =2$, $v^2=0.1$, and two different values of $U$. We also plot the effective bath hybridization function (${\underline{\Delta }}_{\mathrm{eff},4}$) obtained with $N_b=4$.

Figure 3

Imaginary part of the impurity and local Green’s function for $U=1$ (left) and $U=4$ (right) and $\Phi =2$.

Figure 4

Scaled current density $j/v^2$ as a function of (a) the bias voltage $\Phi$, for different values of $U$ and $v^2=0.1$, and (b) the interaction $U$, for different values of the hybridization $v$ and $\Phi =2$.