Exact interacting Green's function for the Anderson impurity at high bias voltages

TL;DR

This paper derives exact high-energy properties of the Anderson impurity model under high bias voltages, mapping it to an effective non-Hermitian Hamiltonian and solving for Green's functions and susceptibilities.

Contribution

It introduces a novel exact solution for the Anderson impurity at high bias, extending the atomic limit with a closed system of equations for Green's functions.

Findings

Charge and current susceptibilities become independent of Coulomb U at high bias.

The spectral weights depend on tunneling asymmetry.

The self-energy captures relaxation processes at high energies.

Abstract

We describe some exact high-energy properties of a single Anderson impurity connected to two noninteracting leads in a nonequilibrium steady state. In the limit of high bias voltages, and also in the high-temperature limit at thermal equilibrium, the model can be mapped on to an effective non-Hermitian Hamiltonian consisting of two sites, which correspond to the original impurity and its image that is defined in a doubled Hilbert space referred to as Liouville-Fock space. For this, we provide a heuristic derivation using a path-integral representation of the Keldysh contour and the thermal field theory, in which the time evolution along the backward contour is replicated by extra degrees of freedom corresponding to the image. We find that the effective Hamiltonian can also be expressed in terms of charges and currents. From this, it can be deduced that the dynamic susceptibilities for the charges and the current fluctuations become independent of the Coulomb repulsion U in the high bias limit. Furthermore, the equation of motions for the Green's function and two other higher-order correlation functions constitute a closed system. The exact solution obtained from the three coupled equations extends the atomic-limit solution such that the self-energy correctly captures the imaginary part caused by the relaxation processes at high energies. The spectral weights of the upper and lower Hubbard levels depend sensitively on the asymmetry in the tunneling couplings to the left and right leads.