Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.03384 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916275898286080 |
|---|---|
| author | Cancès, Éric Kirsch, Alfred Perrin-Roussel, Solal |
| author_facet | Cancès, Éric Kirsch, Alfred Perrin-Roussel, Solal |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A mathematical analysis of IPT-DMFT Cancès, Éric Kirsch, Alfred Perrin-Roussel, Solal Mathematical Physics 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). |
| title | A mathematical analysis of IPT-DMFT |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2406.03384 |