Coherence in the two-impurity Kondo problem

We use the Wilson's renormalization group method to investigate the splitting of the even and odd Kondo resonances in the problem of two interacting Kondo impurities which presages the band-width or the coherence scale in the heavy-Fermion lattice. A finite splitting requires both potential scattering V which lifts particle-hole degeneracy and a difference between the exchange in the even and the odd parity channels(Je-Jo)[1]. We also investigate the elimination of the quantum critical point in the two-impurity Kondo problem[2] due to loss of particle-hole symmetry. [1] I. Affleck and A. W. W. Ludwig, Phys. Rev. Lett. 68, 1046(1992). [2] B. A. Jones, C. M. Varma, and J. W. Wilkins, Phys. Rev. Lett. 61, 125(1988).