Tunneling in quantum wires II: A new line of IR fixed points

TL;DR

This paper investigates new integrable cases of tunneling in quantum wires, focusing on a specific phase diagram where the double sine-Gordon model applies, and computes exact transport properties revealing unique IR fixed points with complete reflection.

Contribution

It identifies and analyzes a new integrable manifold in quantum wire tunneling, expanding understanding of phase diagrams and fixed points with exact transport calculations.

Findings

IR fixed points exhibit complete reflection of charge and spin currents.

Approach to fixed points involves irrelevant operators transferring charge or spin but not both.

Transport properties are exactly computed for the integrable double sine-Gordon model.

Abstract

In a previous paper, we showed that the problem of tunneling in quantum wires was integrable in the isotropic case $g_\sigma=2$. In the present work, we continue the exploration of the general phase diagram by looking for other integrable cases. Specifically, we discuss in details the manifold $g_\rho+g_\sigma=2$, where the associated ``double sine-Gordon'' model is integrable. Transport properties are exactly computed. Surprisingly, the IR fixed points, while having complete reflection of charge and spin currents, do not correspond to two separate leads. Their main characteristic is that they are approached along irrelevant operators of dimension $1+{1\over g_\rho}$ and $1+{1\over g_\sigma}$, corresponding to transfer of one electron charge but no spin, or one spin 1/2 but no charge.