Chiral Y-junction of Luttinger liquid wires at weak coupling: lines of stable fixed points

TL;DR

This paper analyzes the transport in a Y-junction of three Luttinger liquid wires with magnetic flux, identifying stable fixed points and how interactions influence the system's fixed point structure.

Contribution

It derives coupled RG equations for the Y-junction system and uncovers lines of stable fixed points under specific interaction conditions, advancing understanding of chiral Luttinger liquid junctions.

Findings

Only one stable fixed point for repulsive interactions, leading to wire separation.

Four fixed points for attractive interactions, with stability depending on interaction strength.

Lines of stable fixed points occur at specific interaction parameter values.

Abstract

We study the transport properties of a system of three Luttinger liquid wires (with different interaction strengths g, g_3), connected through a Y-junction (main wire and tunneling tip) threaded by magnetic flux, within the scattering state formalism. The scattering matrix and the matrix of conductances are parametrized by three variables. For these we derive coupled RG equations, up to second order in the interaction. The fixed point structure of these equations is analyzed in detail. For repulsive interaction (g, g_3>0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g<0 and/or g_3<0) four fixed points are found, whose stability depends on the interaction strength. For special values of the interaction parameters (a) g=0, g_3<0 or (b) g_3+g^2/2=0 and g<0 we find whole lines of stable fixed points. In certain regions of the g-g_3-plane the RG flow is towards a fixed point without chirality, implying that the effect of the magnetic flux is completely screened.