Unconventional bosonization of chiral quantum wires coupled through a point-contact driven out of equilibrium

TL;DR

This paper introduces an unconventional bosonization method for chiral quantum wires with a point contact out of equilibrium, accurately reproducing Green functions and tunneling characteristics, and demonstrating internal consistency and potential universal scaling.

Contribution

The paper develops a novel non-chiral bosonization technique that accurately models out-of-equilibrium chiral quantum wires with point contacts, aligning with exact solutions and scaling predictions.

Findings

Reproduces exact Green functions for the system

Derives tunneling I-V characteristics from bosonized Green functions

Shows internal consistency of the unconventional bosonization scheme

Abstract

Non-chiral bosonization technique adapted to study chiral quantum wires with non-interacting fermions coupled through a point-contact with a constant bias between the wires is introduced and is shown to reproduce the exact Green functions of this system which was previously derived by the present authors analytically using standard methods. The tunneling I-V characteristics are obtained using the bosonized Green functions. The proposed unconventional bosonization scheme is also shown to be internally consistent as the four-point functions evaluated using NCBT are shown to be related to the two-point functions through Wick's theorem as it should be. In equilibrium, the equal space-time NCBT Green functions for an interacting Luttinger liquid with impurities obtained in a previous work shows universal scaling behaviour in accordance with Bethe ansatz and functional renormalization group predictions. We expect to obtain a similar scaling form of the tunneling properties out of equilibrium in presence of interparticle interactions.