Large-orbital-degeneracy expansion for the lattice Anderson model

Abstract

We study the low-temperature Anderson lattice Hamiltonian via an ‘‘auxiliary-boson’’ 1/N expansion that generalizes to a lattice an approach previously used to study one Anderson impurity. We set up the formalism needed and show that infrared divergences cancel in physical quantities. We show that as far as low-energy excitations are concerned the model behaves like a ‘‘heavy’’ Fermi liquid with a Fermi temperature determined essentially by the one-impurity Kondo temperature. We compute thermodynamic quantities including the Wilson ratio, we study the electron wave functions in the ground state of the lattice and compare them with the wave functions in the ground state of the one-impurity problem, we discuss the question of which physical quantities involve the ‘‘mass enhancement’’ present in the thermodynamics, we compute the spin-spin and density-density correlation functions, and we discuss the frequency- and temperature-dependent conductivity, obtaining results in qualitative agreement with experiment.