{
  "id": "2109.04723",
  "version": "v1",
  "published": "2021-09-10T08:10:28.000Z",
  "updated": "2021-09-10T08:10:28.000Z",
  "title": "Dynamical Mean-Field Theory of Disordered Electrons: Coherent Potential Approximation and Beyond",
  "authors": [
    "Václav Janiš"
  ],
  "comment": "30 pages, Lecture Notes for the Autumn School on Correlated Electrons: The Physics of Correlated Insulators, Metals, and Superconductors, 25-29 September 2017, Forschungszentrum J\\\"ulich (https://www.cond-mat.de/events/correl17/)",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body systems by using many-body Green functions. The many-body approach is used to derive the coherent-potential approximation and to show how it fits into the dynamical mean-field theory. The generating functional of the coherent-potential approximation is obtained in an analytic form from the limit to infinite dimensions of the general many-body description of non-interacting electrons in random lattices. The analytic generating functional of the mean-field description of random systems is extended to the Falicov-Kimball model with thermally equilibrated scattering lattice potential. The many-body Green functions are then used to calculate transport properties. The electrical conductivity of the coherent-potential approximation is derived from the two-particle Green function calculated in infinite spatial dimensions. Finally, a perturbation theory for the vertex corrections to the mean-field conductivity is introduced. In particular, it is shown how to make the expansion beyond the local approximations conserving.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-10T08:10:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical mean-field theory",
      "coherent potential approximation",
      "disordered electrons",
      "equilibrated scattering lattice potential",
      "many-body green functions"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}