Efficient energy resolved quantum master equation for transport\n calculations in large strongly correlated systems

We introduce a systematic approximation for an efficient evaluation of\nBorn--Markov master equations for steady state transport studies in open\nquantum systems out of equilibrium: the energy resolved master equation\napproach. The master equation is formulated in the eigenbasis of the open\nquantum system and build successively by including eigenstates with increasing\ngrandcanonical energies. In order to quantify convergence of the approximate\nscheme we introduce quality factors to check preservation of trace, positivity\nand hermiticity.\n Furthermore, we discuss different types of master equations that go beyond\nthe commonly used secular approximation in order to resolve coherences between\nquasi--degenerate states. For the discussion of complete positivity we\nintroduce a canonical Redfield-Bloch master equation and compare it to a\npreviously derived master equations in Lindblad form with and without using the\nsecular approximation. The approximate scheme is benchmarked for a six orbital\nquantum system which shows destructive quantum interference under the\napplication of a bias voltage. The energy resolved master equation approach\npresented here makes quantum transport calculations in many--body quantum\nsystems numerically accessible also beyond six orbitals with a full Hilbert\nspace of the order of $\\sim 10^6$.\n