G. Zarand et J. Von Delft, Analytical calculation of the finite-size crossover spectrum of the anisotropic two-channel Kondo model, PHYS REV B, 61(10), 2000, pp. 6918-6933
We present a conceptually simple, analytical calculation of the finite-size
crossover spectrum of the anisotropic two-channel Kondo (2CK) model at its
Toulouse point. We use Emery and Kivelson's method, generalized in two way
s. First, we construct all boson fields and Klein factors explicitly in ter
ms of the model's original fermion operators and, secondly, we clarify expl
icitly how the Klein factors needed when refermionizing act on the original
Fock space. This enables us to follow the evolution of the 2CK model's fre
e-fermion states to its exact eigenstates for arbitrary magnetic fields and
spin-flip coupling strengths. We thus obtain an analytic description of th
e crossover of the finite-size spectrum to the non-Fermi-liquid fixed point
, where we recover the conformal field theory results (implying a direct pr
oof of Affleck and Ludwig's fusion hypothesis). From the finite-size spectr
um we extract the operator content of the 2CK fixed point and the dimension
of various relevant and irrelevant perturbations. Our method can easily be
generalized to include various symmetry-breaking perturbations, and to stu
dy the crossover to other fixed points produced by these. Furthermore, it e
stablishes instructive connections between different renormalization group
schemes. We also apply our method to the single-channel Kondo model.