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arXiv · 2406.03384

A mathematical analysis of IPT-DMFT

Éric Cancès·Alfred Kirsch·Solal Perrin-Roussel
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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).

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Éric Cancès, Alfred Kirsch, Solal Perrin-Roussel. 2024-06-05. A mathematical analysis of IPT-DMFT. https://arxiv.org/abs/2406.03384

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