Quantum phase transition of Ising-coupled Kondo impurities

TL;DR

This paper studies a model of two Ising-coupled Kondo impurities, revealing a quantum phase transition between singlet and doublet phases with distinct conductance behaviors, using analytical and numerical methods.

Contribution

It introduces a mapping to a generalized Anderson model and characterizes the phase diagram and conductance at the quantum phase transition.

Findings

Identifies a Kosterlitz-Thouless quantum phase transition.

Determines conductance behavior at the transition, including a universal value.

Analyzes thermodynamics showing a two-step entropy quench.

Abstract

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G = e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization group calculations. In the singlet phase close to the quantum phase transtion, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic mini-domain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.