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A mathematical analysis of IPT-DMFT
- Publication Year :
- 2024
-
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).<br />Comment: 40 pages, 5 figures
- Subjects :
- Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.03384
- Document Type :
- Working Paper