Dynamical Mean Field Theory for nonequilibrium systems in steady state: an auxiliary Lindblad Master Equation approach

We present an approach to compute electronic steady state properties
of strongly correlated quantum systems out of equilibrium
within dynamical mean-field theory (DMFT).
Specifically, the DMFT impurity solver is based upon the exact
solution of an auxiliary system consisting of a small number of bath
sites coupled to the interacting impurity and to two Markovian
reservoirs.
The steady state Green's function of the auxiliary system is
obtained via a biconjugate Lanczos diagonalisation of the corresponding many-body
non-Hermitian Lindblad equation.
The approach can be regarded as the non-equilibrium extension
of the exact-diagonalization based DMFT, and introduces appropriate
absorbing boundary conditions for a many-body system.
Results are also presented for the Anderson
impurity model under a finite bias voltage, and the behavior of
the Kondo peak as function of voltage is discussed.