Finite-Size Bosonization of 2-Channel Kondo Model: a Bridge between Numerical Renormalization Group and Conformal Field Theory

TL;DR

This paper extends the bosonization approach to the 2-channel Kondo model for finite systems, connecting numerical and conformal field theory methods to analyze its spectrum and eigenstates.

Contribution

It provides an exact finite-size spectrum and eigenstates for the 2-channel Kondo model, bridging bosonization, NRG, and CFT techniques.

Findings

Finite-size spectrum matches CFT predictions.

Eigenstates constructed analytically at finite size.

Spectrum crossover from non-Fermi-liquid to Fermi-liquid with magnetic field.

Abstract

We generalize Emery and Kivelson's (EK) bosonization-refermionization treatment of the 2-channel Kondo model to finite system size and on the EK-line analytically construct its exact eigenstates and finite-size spectrum. The latter crosses over to conformal field theory's (CFT) universal non-Fermi-liquid spectrum (and yields the most-relevant operators' dimensions), and further to a Fermi-liquid spectrum in a finite magnetic field. Our approach elucidates the relation between bosonization, scaling techniques, the numerical renormalization group (NRG) and CFT. All CFT's Green's functions are recovered with remarkable ease from the model's scattering states.