Junctions of multiple quantum wires with different Luttinger parameters

TL;DR

This paper analyzes the conductance properties of junctions of multiple quantum wires with different interaction strengths, combining boundary conformal field theory and numerical density-matrix-renormalization-group methods.

Contribution

It provides analytical phase diagrams and conductance calculations for multi-wire junctions with varying Luttinger parameters, supported by numerical validation.

Findings

Good agreement between numerical and analytical results for two-wire junctions.

Complete phase diagram for three-wire Y junctions as a function of Luttinger parameters.

Explicit conductance values at stable fixed points for different wire configurations.

Abstract

Within the framework of boundary conformal field theory, we evaluate the conductance of stable fixed points of junctions of two and three quantum wires with different Luttinger parameters. For two wires, the physical properties are governed by a single effective Luttinger parameters for each of the charge and spin sectors. We present numerical density-matrix-renormalization-group calculations of the conductance of a junction of two chains of interacting spinless fermions with different interaction strengths, obtained using a recently developed method [Phys. Rev. Lett. 105, 226803 (2010)]. The numerical results show very good agreement with the analytical predictions. For three spinless wires, i.e., a Y junction, we analytically determine the full phase diagram, and compute all fixed-point conductances as a function of the three Luttinger parameters.