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Abstract

The functional renormalization group (FRG) provides a flexible tool to study correlations in low-dimensional electronic systems. In this paper, we present an FRG approach to the steady state of quantum wires out of thermal equilibrium. Our method is correct up to second order in the two-particle interaction and accounts for inelastic scattering. We combine semianalytic solutions of the flow equations with MPI parallelization techniques, which allows us to treat systems of up to 60 lattice sites. The equilibrium limit is well understood and serves as a benchmark. We compute effective distribution functions, the local density of states, and the steady-state current and demonstrate that all of these quantities depend strongly on the choice of the cutoff employed within the FRG. Nonequilibrium is plagued by the lack of physical arguments in favor of a certain cutoff as well as by the appearance of secular higher-order terms which are only partly included in our approach. This demonstrates the inadequacy of a straightforward second-order FRG scheme to study interacting quantum wires out of equilibrium in the absence of a natural cutoff choice.