Auxiliary master equation approach for correlated quantum impurities out of equilibrium

The auxiliary master equation approach [1,2] allows for an accurate and efficient treatment of
correlated impurities out of equilibrium. The method 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 intervening auxiliary orbitals allow for a treatment of non-Markovian
dynamics at the impurity. The time dependence of this auxiliary system is controlled by a
Lindblad master equation whose parameters are used to optimize the mapping. The auxiliary
system exponentially approaches the original impurity problem upon increasing the number
of parameters, i.e. of bath orbitals. Green’s functions are evaluated via (non-hermitian)
Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, our
MPS implementation produces highly accurate spectral functions for nonequilibrium correlated
impurity problems in the Kondo regime. Specifically, we can treat large values of the interaction
and low temperatures T , well below the Kondo scale T K . For T = T K /4 and T = T K /10 we find
a splitting of the Kondo resonance into a two-peak structure at bias voltages just above T K . The
approach turns out to be an efficient impurity solver in equilibrium as well: a benchmark of our
results for T = T K /4 reveals a remarkably close agreement to numerical renormalization group.
Applications to nonequilibrium dynamical mean-field-theory [4] as well as an implementation
within Floquet theory for periodic driving [5] will be discussed as well.
References
[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)
[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)
[3] A. Dorda et al., PRB 92, 125145 (2015)
[4] I. Titvinidze et al., PRB 92, 245125 (2015)
[5] M. Sorantin et al., in preparation.