Solution of the two impurity, two channel Kondo Model

We solve the two-impurity two-channel Kondo model using a combination of conformal invariance and bosonisation techniques. The odd-even symmetric case is analysed in detail. The RKKY interaction turns out to be exactly marginal, resulting in a line of non-Fermi liquid fixed points. Explicit formulae are given for the critical exponents and for the finite-size spectrum, which depend continuously on a single parameter. The marginal line spans a range of values of the RKKY coupling $I$ which goes from the infinitely strong ferromagnetic point $I=-\infty$ (associated with a 4-channel spin-1 Kondo model) to a finite antiferromagnetic critical value $I_c>0$ beyond which a Fermi liquid is recovered. We also find that, when the odd-even symmetry is broken, the marginal line is unstable for ferromagnetic $I$, while for antiferromagnetic $I$ it extends into a manifold of fixed points.