Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit

TL;DR

This paper introduces a new stable fixed point in a Luttinger liquid with a scatterer, revealing universal behavior dominated by a Goldstone mode, with unique scattering and noise properties, offering an alternative to existing models.

Contribution

It identifies a novel paradigmatic limit in Luttinger liquids with incoherent scatterers, characterized by equal scattering probabilities and vanishing shot noise, expanding understanding of impurity effects.

Findings

Universal behavior governed by a Goldstone mode

Equal probabilities for forward and backward scattering

Vanishing shot noise and zero cross-current correlations

Abstract

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: a Goldstone mode dominates the low energy dynamics, leading to a universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this non-trivial scattering pattern, we find that the shot noise as well as zero cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.