Solution of effective Hamiltonian of impurity hopping between two sites in a metal

We analyze in detail all the possible fixed points of the effective Hamiltonian of a non-magnetic impurity hopping between two sites in a metal obtained by Moustakas and Fisher (MF) in Ref.9. We find a non-fermi liquid fixed line which continuously interpolates between the 2-channel Kondo fixed point(2CK) and the one channel, two impurity Kondo (2IK) fixed point. Although the finite size spectrum and the coefficient of the electrical resistivity depend on the position on the fixed line, the thermodynamic quantities and the exponent of the electron resistivity do not and show the same behaviors as the 2CK. The additional non-fermi liquid fixed point found by MF has the same symmetry as the 2IK, the thermodynamic quantities show fermi liquid behaviors Cimp ∼ T 2, χimp ∼ const., but the electrical resistivity goes linear as T . The system is shown to flow to a stable fermi-liquid fixed line which continuously interpolates between the non-interacting fixed point and the 2 channel spin-flavor Kondo fixed point (2CSFK) discussed by the author in Ref.22. The conditions to observe the non-fermi liquid behaviors controlled by the zero temperature non-fermi liquid fixed line are discussed. Finally the implications are given for a non-magnetic impurity hopping around three sites