Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.21287 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908381487300608 |
|---|---|
| author | Cancès, E. Kirsch, A. Perrin--Roussel, S. |
| author_facet | Cancès, E. Kirsch, A. Perrin--Roussel, S. |
| contents | In a previous contribution (E. Cancès, A. Kirsch and S. Perrin--Roussel, arXiv:2406.03384), we have proven the existence of a solution to the Dynamical Mean-Field Theory (DMFT) equations under the Iterated Perturbation Theory (IPT-DMFT) approximation. In view of numerical simulations, these equations need to be discretized. In this article, we are interested in a discretization of the \acrshort{ipt}-\acrshort{dmft} functional equations, based on the restriction of the hybridization function and local self-energy to a finite number of points in the upper half-plane $\left(iω_n\right)_{n \in |[0,N_ω]|}$, where $ω_n=(2n+1)π/ β$ is the $n$-th Matsubara frequency and $N_ω\in \mathbb N$. We first prove the existence of solutions to the discretized equations in some parameter range depending on $N_ω$. We then prove uniqueness for a smaller range of parameters. We also study more in depth the case of bipartite systems exhibiting particle-hole symmetry. In this case, the discretized IPT-DMFT equations have purely imaginary solutions, which can be obtained by solving a real algebraic system of $(N_ω+1)$ equations with $(N_ω+1)$ variables. We provide a complete characterization of the solutions for $N_ω=0$ and some results for $N_ω=1$ in the simple case of the Hubbard dimer. We finally present some numerical simulations on the Hubbard dimer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mathematical analysis of the discretized IPT-DMFT equations Cancès, E. Kirsch, A. Perrin--Roussel, S. Numerical Analysis In a previous contribution (E. Cancès, A. Kirsch and S. Perrin--Roussel, arXiv:2406.03384), we have proven the existence of a solution to the Dynamical Mean-Field Theory (DMFT) equations under the Iterated Perturbation Theory (IPT-DMFT) approximation. In view of numerical simulations, these equations need to be discretized. In this article, we are interested in a discretization of the \acrshort{ipt}-\acrshort{dmft} functional equations, based on the restriction of the hybridization function and local self-energy to a finite number of points in the upper half-plane $\left(iω_n\right)_{n \in |[0,N_ω]|}$, where $ω_n=(2n+1)π/ β$ is the $n$-th Matsubara frequency and $N_ω\in \mathbb N$. We first prove the existence of solutions to the discretized equations in some parameter range depending on $N_ω$. We then prove uniqueness for a smaller range of parameters. We also study more in depth the case of bipartite systems exhibiting particle-hole symmetry. In this case, the discretized IPT-DMFT equations have purely imaginary solutions, which can be obtained by solving a real algebraic system of $(N_ω+1)$ equations with $(N_ω+1)$ variables. We provide a complete characterization of the solutions for $N_ω=0$ and some results for $N_ω=1$ in the simple case of the Hubbard dimer. We finally present some numerical simulations on the Hubbard dimer. |
| title | A mathematical analysis of the discretized IPT-DMFT equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.21287 |