Functional expansion of the Anderson and SU(N) lattice models

Abstract

We employ the functional expansion of Kadanoff and Baym to study the Anderson and SU( N) lattice models in the infinite correlation limit ( U→∞). We use Hubbard operators that describe real localized electrons and forbid their double occupation at each site. In the lowest nontrivial approximation, our expressions are similar to (but different from) those derived by several ‘effective Hamiltonian’ techniques, like the Mean Field Slave Boson (MFSB). In the usual large N limit, our results coincide with those of the equations of motion and Brillouin-Wigner expansions, which are exact in that limit. Our results at T = 0 K are compared to those of the MFSB quasiparticle description, and we discuss the two approximations in the region in which they are different. We conclude that the two treatments are complementary: the quasiparticle description should give better results for the thermodynamic properties but our treatment describes in a more physical way the overall behavior of the spectral density of the localized electrons. The Kondo resonance is not obtained in our treatment, and we conjecture that it should appear in a higher-order approximation.