Solution of the two-impurity Kondo model: critical point, Fermi-liquid phase, and crossover

TL;DR

This paper provides an asymptotically exact solution for the two-impurity Kondo model, identifying the critical point, describing the Fermi-liquid phase, and deriving crossover functions, with implications for understanding quantum impurity systems.

Contribution

It introduces a controlled, exact solution for the two-impurity Kondo model near the critical point, including an effective Hamiltonian and crossover functions.

Findings

Explicit identification of the critical point and its physical origin.

Exact solution of the effective Hamiltonian in both critical and Fermi-liquid phases.

Derived analytic crossover functions for specific heat and susceptibility.

Abstract

An asymptotically exact solution is presented for the two-impurity Kondo model for a finite region of the parameter space surrounding the critical point. This region is located in the most interesting intermediate regime where RKKY interaction is comparable to the Kondo temperature. After several exact simplifications involving reduction to one dimension and abelian bosonization, the critical point is explicitly identified, making clear its physical origin. By using controlled low energy projection, an effective Hamiltonian is mapped out for the finite region in the phase diagram around the critical point. The completeness of the effective Hamiltonian is rigorously proved from general symmetry considerations. The effective Hamiltonian is solved exactly not only at the critical point but also for the surrounding Fermi-liquid phase. Analytic crossover functions from the critical to Fermi-liquid behavior are derived for the specific heat and staggered susceptibility. It is shown that applying a uniform magnetic field has negligible effect on the critical behavior.