{
  "id": "2406.03384",
  "version": "v1",
  "published": "2024-06-05T15:36:39.000Z",
  "updated": "2024-06-05T15:36:39.000Z",
  "title": "A mathematical analysis of IPT-DMFT",
  "authors": [
    "Éric Cancès",
    "Alfred Kirsch",
    "Solal Perrin-Roussel"
  ],
  "comment": "40 pages, 5 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide a mathematical analysis of the Dynamical Mean-Field Theory, a celebrated representative of a class of approximations in quantum mechanics known as embedding methods. We start by a pedagogical and self-contained mathematical formulation of the Dynamical Mean-Field Theory equations for the finite Hubbard model. After recalling the definition and properties of one-body time-ordered Green's functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe a specific impurity solver, namely the Iterated Perturbation Theory solver, which can be conveniently formulated using Matsubara's Green's functions. Within this framework, we prove under certain assumptions that the Dynamical Mean-Field Theory equations admit a solution for any set of physical parameters. Moreover, we establish some properties of the solution(s).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T15:36:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mathematical analysis",
      "dynamical mean-field theory equations admit",
      "iterated perturbation theory solver",
      "finite hubbard model",
      "one-body time-ordered greens functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}