Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results

TL;DR

This paper uses conformal field theory to analyze the two-impurity Kondo problem, clarifying conditions for a non-Fermi liquid critical point and comparing theoretical predictions with numerical renormalization group results.

Contribution

It identifies the specific particle-hole symmetry condition necessary for the critical point and applies boundary conformal field theory to analyze the finite-size spectrum.

Findings

Critical particle-hole symmetry condition for the non-Fermi liquid point

Detailed finite-size spectrum matching NRG results

Analysis of Green's functions and hidden symmetries

Abstract

Numerical renormalization group and conformal field theory work indicate that the two impurity Kondo Hamiltonian has a non-Fermi liquid critical point separating the Kondo-screening phase from the inter-impurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurance of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyse this critical point using the boundary conformal field theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behaviour, and a hidden $SO(7)$ are analysed.