Steady-state dynamical mean-field theory within an auxiliary master equation approach

Abstract: We present a method to compute electronic steady state properties of
strongly correlated quantum systems out of equilibrium within dynamical mean-
�eld theory (DMFT) [1]. The DMFT correlated impurity problem is mapped onto
an auxiliary open system consisting of a small number of bath orbitals coupled to
the interacting impurity and to Markovian reservoirs described by a generalized
Lindblad equation [2,3]. The parameters of the auxiliary open system are used
to optimize the mapping, which becomes exponentially exact upon increasing the
number of bath orbitals. The auxiliary system is then solved by exact diagonali-
sation of the corresponding many-body non-Hermitian Lindblad equation, which
allows to evaluate Green’s functions directly in steady state upon bypassing the ini-
tial transient dynamics [3]. 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 out of equilibrium.
[1] J.K. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006) [2] E. Arrigoni et al.,Phys. Rev. Lett. 110, 086403 (2013) [3] A. Dorda et al., Phys. Rev. B 89, 165105
(2014).