A Single Impurity in Tomonaga-Luttinger Liquids

TL;DR

This paper analyzes how a single impurity affects the low-temperature behavior of one-dimensional Tomonaga-Luttinger liquids with repulsive interactions, revealing complex renormalization group flow and multiple fixed points.

Contribution

It provides a detailed analysis of the renormalization group flow for impurities in Tomonaga-Luttinger liquids, identifying new fixed points beyond the known weakly connected wire states.

Findings

Complex RG flow diagram with multiple fixed points.

Identification of fixed points controlling low-temperature physics.

Impurity potential strength influences low-energy behavior.

Abstract

The problem of a single impurity in one dimensional Tomonaga-Luttinger liquids with a repulsive electron-electron interaction is discussed. We find that the renormalization group flow diagram for the parameters characterizing the impurity is rather complex. Apart from the fixed points corresponding to two weakly connected semi-infinite wires, the flow diagram contains additional fixed points which control the low temperature physics when the bare potential of the impurity is not strong.