Chiral Y-junction of Luttinger liquid wires at strong coupling: fermionic representation

TL;DR

This paper analyzes the conductance properties of a three-wire chiral Y-junction of spinless Luttinger liquids using fermionic scattering states, deriving RG equations and identifying fixed points for various interaction regimes.

Contribution

It introduces a fermionic scattering state approach to calculate conductances and derives RG equations for arbitrary interactions in multi-wire junctions, revealing new fixed points and correcting previous conjectures.

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.

Confirmation of weak-coupling fixed points extending into strong coupling, and discovery of new fixed points.

Abstract

We calculate the conductances of a three-terminal junction set-up of spinless Luttinger liquid wires threaded by a magnetic flux, allowing for different interaction strength g_3 != g in the third wire. We employ the fermionic representation in the scattering state picture, allowing for a direct calculation of the linear response conductances, without the need of introducing contact resistances at the connection points to the outer ideal leads. The matrix of conductances is parametrized by three variables. For these we derive coupled renormalization group (RG) equations, by summing up infinite classes of contributions in perturbation theory. The resulting general structure of the RG equations may be employed to describe junctions with an arbitrary number of wires and arbitrary interaction strength in each wire. The fixed point structure of these equations (for the chiral Y-junction) 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, the stability of which depends on the interaction strength. We confirm our previous weak-coupling result of lines of fixed points for special values of the interaction parameters reaching into the strong coupling domain. We find new fixed points not discussed before, even at the symmetric line g=g_3, at variance with the results of Oshikawa et al. The pair tunneling phenomenon conjectured by the latter authors is not found by us.