Perturbation of infra-red fixed points and duality in quantum impurity problems

TL;DR

This paper develops a perturbation theory around the infra-red fixed point for integrable quantum impurity problems, providing detailed low-temperature expansions and revealing a duality between UV and IR regimes in tunneling phenomena.

Contribution

It introduces a meaningful irrelevant perturbation theory around the IR fixed point and demonstrates a duality in quantum impurity problems, extending understanding beyond traditional models.

Findings

Complete low-temperature resistivity expansion for the Kondo model.

Exact duality between UV and IR regimes in tunneling current.

Connection between duality and integrability, with instantons expansion.

Abstract

We explain in this paper how a meaningful irrelevant perturbation theory around the infra-red (strong coupling) fixed point can be carried out for integrable quantum impurity problems. This is illustrated in details for the spin 1/2 Kondo model, where our approach gives rise to the complete low temperature expansion of the resistivity, beyond the well known $T^2$ Fermi liquid behaviour. We also consider the edge states tunneling problem, and demonstrate by Keldysh techniques that the DC current satisfies an exact duality between the UV and IR regimes. This corresponds physically to a duality between the tunneling of Laughlin quasi particles and electrons, and, more formally, to the existence of an exact instantons expansion. The duality is deeply connected with integrability, and could not have been expected a priori.