Bosonization of one dimensional fermions out of equilibrium

TL;DR

This paper develops a bosonization method for non-equilibrium one-dimensional fermions using the Keldysh formalism, enabling analysis of interacting quantum wires and electron Green functions under arbitrary energy distributions.

Contribution

It introduces a novel bosonization approach for out-of-equilibrium fermions, connecting Green functions to functional determinants and exploring effects like fractionalization and dephasing.

Findings

Green functions expressed as functional determinants of counting operators

Dephasing rates oscillate with interaction strength for double-step distributions

Method applicable to spinful particles and spatially separated Green functions

Abstract

Bosonization technique for one-dimensional fermions out of equilibrium is developed in the framework of the Keldysh action formalism. We first demonstrate how this approach is implemented for free fermions and for the problem of non-equilibrium Fermi edge singularity. We then employ the technique to study an interacting quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green functions, which can be measured via tunneling spectroscopy technique and carry the information about energy distribution, zero-bias anomaly, and dephasing, are expressed in terms of functional determinants of single-particle "counting" operators. The corresponding time-dependent scattering phase is found to be intrinsically related to "fractionalization" of electron-hole excitations in the tunneling process and at boundaries with leads. Results are generalized to the case of spinful particles as well to Green functions at different spatial points (relevant to the problem of dephasing in Luttinger liquid interferometers). For double-step distributions, the dephasing rates are oscillatory functions of the interaction strength.