Intermediate fixed point in a Luttinger liquid with elastic and dissipative backscattering

TL;DR

This paper investigates a Luttinger liquid with both elastic and dissipative backscattering, revealing a stable intermediate fixed point where current is evenly split, which is a new paradigm differing from previous models.

Contribution

It provides a non-perturbative analysis of the RG flows and fixed points in a Luttinger liquid with complex scattering, including Klein factors and instanton calculations, identifying a novel stable intermediate fixed point.

Findings

Identifies a stable intermediate fixed point with equal current splitting.

Shows the fixed point is stable for Luttinger parameter g<1.

Employs non-perturbative instanton analysis including Klein factors.

Abstract

In a recent work [Phys. Rev. Lett. {\bf 108}, 136401 (2012)] we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a new paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed point landscape, and scaling near those fixed points. Our analysis is non-perturbative in the elastic tunneling amplitudes, employing an instanton calculation in one or two of the available elastic tunneling channels. Our analysis accounts for non-trivial Klein factors, which represent anyonic or fermionic statistics. These Klein factors need to be taken into account due to the fact that higher order tunneling processes take place. In particular we find a stable fixed point, where an incoming current is split ${1 \over 2}$ - $1\over 2$ between a forward and a backward scattered beams. This intermediate fixed point, between complete backscattering and full forward scattering, is stable for the Luttinger parameter $g<1$.