Diagrammatic method for investigating universal behavior of impurity systems
arXiv:cond-mat/9807134 · doi:10.1103/PhysRevB.55.13575
Abstract
The universal behavior of magnetic impurities in a metal is proved with the help of skeleton diagrams. The energy scales are derived from the structure of the skeleton diagrams. A minimal set of skeleton diagrams is sorted out that scales exactly. For example, the non-crossing approximation for the Anderson impurity model can describe the crossover phenomenon. The universal Wilson-number is calculated within the non-crossing approximation. The method allows for an assessment of various approximations for impurity Hamiltonians.
21 pages, 3 figures