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The functional renormalization group (FRG) provides a flexible tool to studycorrelations in low-dimensional electronic systems. In this paper, we present anovel FRG approach to the steady-state of quantum wires out of thermalequilibrium. Our method is correct up to second order in the two-particleinteraction and accounts for inelastic scattering. We combine semi-analyticsolutions of the flow equations with MPI parallelization techniques, whichallows us to treat systems of up to 60 lattice sites. The equilibrium limit iswell-understood and serves as a benchmark. We compute effective distributionfunctions, the local density of states, and the steady-state current anddemonstrate that all of these quantities depend strongly on the choice of thecutoff employed within the FRG. Non-equilibrium is plagued by the lack ofphysical arguments in favor of a certain cutoff as well as by the appearance ofsecular higher-order terms which are only partly included in our approach. Thisdemonstrates the inadequacy of a straightforward second-order FRG scheme tostudy interacting quantum wires out of equilibrium in the absence of a naturalcutoff choice.

Second-order functional renormalization group approach to quantum wires out of equilibrium