2008/04/21 by Norbert Grewe, Sebastian Schmitt, Torben Jabben +2
Physics and Astronomy · #Advanced Chemical Physics Studies #Physics of Superconductivity and Magnetism #Rare-earth and actinide compounds #cond-mat.str-el
paper · pdf · doi:10.1088/0953-8984/20/36/365217
published as J. Phys.: Condens. Matter 20 (2008) 365217 · 45 pages, 22 figures
arxiv created 2008/04/21 · openalex publication_date 2008/08/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
For the treatment of interacting electrons in crystal lattices approximations based on the picture of effective sites, coupled in a self-consistent fashion, have proven very useful. Particularly in the presence of strong local correlations, a local approach to the problem, combining a powerful method for the short ranged interactions with the lattice propagation part of the dynamics, determines the quality of results to a large extent. For a considerable time the non crossing approximation (NCA) in direct perturbation theory, an approach originally developed by Keiter for the Anderson impurity model, built a standard for the description of the local dynamics of interacting electrons. In the last couple of years exact methods like the numerical renormalization group (NRG) as pioneered by Wilson, have surpassed this approximation as regarding the description of the low energy regime. We present an improved approximation level of direct perturbation theory for finite Coulomb repulsion U, the crossing approximation one (CA1) and discuss its connections with other generalizations of NCA. CA1 incorporates all processes up to fourth order in the hybridization strength V in a self-consistent skeleton expansion, retaining the full energy dependence of the vertex functions. We reconstruct the local approach to the lattice problem from the point of view of cumulant perturbation theory in a very general way and discuss the proper use of impurity solvers for this purpose. Their reliability can be tested in applications to e.g. the Hubbard model and the Anderson-lattice model. We point out shortcomings of existing impurity solvers and improvements gained with CA1 in this context. This paper is dedicated to the memory of Hellmut Keiter.