Effective equilibrium theory of nonequilibrium quantum transport

The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. Here, we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [S. Hershfield, Phys. Rev. Lett. 70 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system’s Lippmann–Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper, we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger–Keldysh framework and the effective equilibrium approach, and relate Green’s functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle–hole symmetric point, we investigate the fate of the Abrikosov–Suhl resonance as a function of bias voltage and magnetic field.

► Reformulation of steady-state nonequilibrium quantum transport, following Hershfield.
► Derivation of effective equilibrium density operator using the “open-system” approach.
► Equivalence with the Keldysh description and formulas relating the two approaches.
► Novel framework to treat interactions perturbatively.
► Application to nonequilibrium Anderson model and fate of Abrikosov–Suhl resonance.