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

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.