  This manuscript aims to compare the so-called iterated perturbation theory
(IPT) and auxiliary master equation approach (AMEA) impurity solvers for a Mott
insulating system driven out of equilibrium by a static electric field.
Electronic heat bath and optical phonons are employed as dissipation mechanism
of the current-induced Joule heat that the excited electrons of the lattice
experience as the result of the field's driving. Despite its simplicity, the
IPT approach yields results which qualitatively are in good agreement with
those obtained within the AMEA impurity solver, although fails to reproduce
some correlation effects.
