Y-junction connecting Luttinger liquids: fixed point structure and conductances

TL;DR

This paper analyzes the transport properties of a Y-junction connecting three Luttinger liquids with varying interactions, deriving RG equations, fixed point structures, and discovering a novel fixed point under strong attractive interactions.

Contribution

It formulates the problem using current algebra, derives coupled RG equations in ladder approximation, and identifies a new fixed point for strong attractive interactions.

Findings

Fixed point structure characterized by two parameters.

Higher order interactions do not alter scaling near fixed points.

Discovery of a new fixed point with unusual properties under strong attraction.

Abstract

We study the transport properties of three Luttinger liquid wires (with possibly different interaction strength), connected through a Y-junction, within the scattering state formalism. We first formulate the problem in current algebra language and focus on the case of a symmetric set-up, for which the scattering matrix and the matrix of conductances is parametrized by two variables. For these we derive coupled RG equations, first in a ladder summation up to infinite order in the interaction. The fixed point structure and the implicit solution of these equations is presented. It is shown that higher order terms beyond the ladder approximation do not change the scaling behavior near the fixed points. For sufficiently strong attractive interaction a new fixed point with unusual properties is found.