Is there more than one type of quantum critical points in heavy-fermion metals?

I review the basic physical picture that has traditionally been associated with the quantum phase transitions in clean heavy fermion metals, as well a s some new questions that have been raised by recent neutron scattering exp eriments. I will then describe the results from an extended dynamical mean- field theory of the Kondo lattice models. Unlike all previous studies of th e model, our approach treats on an equal footing the quantum fluctuations a ssociated with both the Kondo and RKKY couplings. Two types of quantum phas e transitions are found - the first a conventional spin-density-wave transi tion, the second driven by local physics. The second type of quantum critic al point appears to have already been seen experimentally. (C) 2001 Elsevie r Science B.V. All rights reserved.