Exact Green's function for a multi-orbital Anderson impurity at high bias voltages

TL;DR

This paper derives an exact nonequilibrium Green's function for a multi-orbital Anderson model at high bias voltages, extending previous spin-only results to arbitrary orbital numbers using an effective non-Hermitian Hamiltonian.

Contribution

It introduces a novel approach using a Liouville-Fock space and an effective non-Hermitian Hamiltonian to analyze high-bias properties for any number of orbitals in the Anderson model.

Findings

Exact Green's function representation with continued fractions

High-bias relaxation processes captured by decay rates

Comparison shows improved accuracy over NCA at high temperatures

Abstract

We study the nonequilibrium Keldysh Green's function for an N-orbital Anderson model at high bias voltages, extending a previous work, which for the case only with the spin degrees of freedom N=2, to arbitrary N. Our approach uses an effective non-Hermitian Hamiltonian that is defined with respect to a Liouville-Fock space in the context of a thermal field theory. The result correctly captures the relaxation processes at high energies, and is asymptotically exact not only in the high-bias limit but also in the high-temperature limit at thermal equilibrium. We also present an explicit continued-fraction representation of the Green's function. It clearly shows that the imaginary part is recursively determined by the decay rate of intermediate states with at most N-1 particle-hole-pair excitations. These high-bias properties follow from the conservations of a generalized charge and current in the Liouville-Fock space. We also examine temperature dependence of the spectral function in equilibrium, comparing the exact results with both the finite-T and infinite-T results of the non-crossing approximation (NCA).