Low energy properties of M-state tunneling systems in metals: New candidates for non-Fermi-liquid systems

Abstract

We construct a generalized multiplicative renormalization group transformation to study the low energy dynamics of a heavy particle tunneling among $M$ different positions and interacting with $N_f$ independent conduction electron channels. Using a $1/N_f$-expansion we show that this M-level scales towards a fixed point equivalent to the $N_f$ channel $SU(M) \times SU(N_f)$ Coqblin-Schrieffer model. Solving numerically the scaling equations we find that a realistic M-level system scales close to this fixed point (FP) and its Kondo temperature is in the experimentally observable range $1-10 K$.