Fermi Surface and Antiferromagnetism in the Kondo Lattice: An Asymptotically Exact Solution in d>1 Dimensions

Interest in the heavy fermion metals has motivated us to examine the quantum phases and their Fermi surfaces within the Kondo lattice model. We demonstrate that the model is soluble asymptotically exactly in any dimension d>1, when the Kondo coupling is small compared with the RKKY interaction and in the presence of antiferromagnetic ordering. We show that the Kondo coupling is exactly marginal in the renormalization group sense, establishing the stability of an ordered phase with a small Fermi surface AF_S. Our results have implications for the global phase diagram of the heavy fermion metals, suggesting a Lifshitz transition inside the antiferromagnetic region and providing a new perspective for a Kondo-destroying antiferromagnetic quantum critical point.