ABSTRACT
The importance of the Bethe Ansatz is not just for providing exact wave-functions, spectra and thermodynamics for models to which it is applicable. As the energy spectrum is obtained for the entire energy range, the thermodynamic results are therefore valid for the entire range of temperatures and magnetic fields. The application of conformal field theory relies upon the hypotheses of conformal 222invariance (that the conformally invariant model corresponding to the special value of λ corresponds with the non-trivial fixed point of the multichannel Kondo model) and fusion rules, as discussed in section 6.1, which are valid only at low temperatures and energies in contrast with the Bethe Ansatz. Strictly speaking these cannot be proved a priori but, by making these assumptions and deriving results, one can then compare with the exact Bethe-Ansatz results to verify the hypotheses. The conformal theory can then be extended to calculate dynamical properties for which the Bethe Ansatz fails. Similar remarks apply to the NCA; as discussed in sections 5.1 and 5.3, the thermodynamic properties of the NCA are in good agreement with exact Bethe-Ansatz results for the overcompensated Kondo models, giving confidence in the dynamics results which are inaccessible to the Bethe Ansatz. (The problem with dynamics is that, while the Bethe Ansatz provides exact many-body wavefunctions, it is an unsolved problem to express properly the operators which couple to external probes, such as the electrical current, in terms of this diagonal basis. In particular, it is not known how to construct scattering state solutions for the Hamiltonian.)
