Solution of the Anderson Model at N→∞ Using TFD of a Quantum Algebra

Abstract

Thermo field dynamics of a quantum algebra is applied to both the single-site and lattice cases of the N-fold degenerate, infinite U, Anderson model. The degenerate nature of the f-electron vacuum leads to a sector structure and vacuum diagrams. Propagators carry self-energies, and a “point-vertex” which arises due to the algebra of the Hubbard operators, and makes the propagators very different from the usual Feynman propagators. In the N→∞ limit, only the tadpole diagrams remain. The single-site case is solved self-consistently in this limit, showing a phase transition to a Kondo state at a temperature, Tκ, which agrees with the usual Kondo temperature. The lattice case, in the N→∞ limit, may be solved self-consistently using a “same-sector” approximation. This yields a phase transition at Tκ to a renormalized two band hybridization with a gap the size of Tκ at the Fermi surface, in agreement with the mean field results.