Auxiliary master equation approach for correlated quantum impurities out of equilibrium

The auxiliary master equation approach [1,2] allows for a direct and ef�cient calculation of steady state properties of
correlated impurities out of equilibrium, as is needed, e.g., for non-equilibrium dynamical mean �eld theory (DMFT). It
is based upon a mapping onto an auxiliary open quantum system in which the impurity is coupled to bath orbitals as well
as to a Markovian environment. The dynamics of this auxiliary system are controlled by a Lindblad master equation whose
parameters are used to optimize the mapping, which quickly becomes exact upon increasing the number of bath orbitals.
Steady state and Green’s functions of the auxiliary system are evaluated by (non-hermitian) Lanczos exact diagonalization
or by matrix-product states (MPS). Dissipation is taken into account already with a small number of bath orbitals. We
discuss steady-state transport properties and spectrum of the Anderson impurity model in the presence of a voltage bias.
The splitting of the Kondo peak as function of voltage is discussed. The approach can be regarded as the non-equilibrium
steady-state extension of the exact-diagonalization or MPS-based DMFT, and introduces appropriate absorbing boundary
conditions for a many-body system.