Pedestrian Approach to the Two-Channel Kondo Model

TL;DR

This paper reformulates the two-channel Kondo model to analyze its non-Fermi liquid fixed point using a strong-coupling expansion, revealing new insights into its quantum states and related lattice models.

Contribution

It introduces a reformulation that explicitly removes charge degrees of freedom, enabling perturbative analysis of the non-Fermi liquid fixed point and exploring the large N limit of O(N) Kondo models.

Findings

Recovery of non-Fermi liquid physics for N=3

Development of a spin-gap in the Kondo lattice model

Identification of marginal Fermi liquid behavior at strong coupling

Abstract

We reformulate the two-channel Kondo model to explicitly remove the unscattered charge degrees of freedom. This procedure permits us to move the non-Fermi liquid fixed point to infinite coupling where we can apply a perturbative strong-coupling expansion. The fixed point Hamiltonian involves a three-body Majorana zero mode whose scattering effects give rise to marginal self-energies. The compactified model is the N=3 member of a family of "O(N)" Kondo models that can be solved by semiclassical methods in the large $N$ limit. For odd $N$, {\em fermionic} "Kink" fluctuations about the $N=\infty$ mean-field theory generate a fermionic $N$-body bound-state which asymptotically decouples at low energies. For N=3, our semi-classical methods fully recover the non-Fermi liquid physics of the original two channel model. Using the same methods, we find that the corresponding O(3) Kondo lattice model develops a spin-gap and a gapless band of coherently propagating three-body bound-states. Its strong-coupling limit offers a rather interesting realization of marginal Fermi liquid behavior.