On the Hartree-Fock phase diagram for the two-dimensional Hubbard model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918261254258688 |
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| author | Charlier, Christophe Langmann, Edwin Lenells, Jonatan |
| author_facet | Charlier, Christophe Langmann, Edwin Lenells, Jonatan |
| contents | We propose an analytical method for the construction of Hartree-Fock phase diagrams for the (fermion) Hubbard model and various generalizations thereof. Such phase diagrams are traditionally constructed numerically, but we argue that, by using asymptotic techniques, it is possible to obtain analytic formulas approximating the curves separating the different phases to very high accuracy. To illustrate the new method, we apply it to the two-dimensional Hubbard model on the square lattice at zero temperature. This yields formulas for the Hartree-Fock phase boundaries that agree with, but also improve on, earlier numerical results. In particular, our results provide the first rigorous proof of the existence of mixed phases in this model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Hartree-Fock phase diagram for the two-dimensional Hubbard model Charlier, Christophe Langmann, Edwin Lenells, Jonatan Mathematical Physics Strongly Correlated Electrons 81T40, 45M05, 81V74, 82D03 We propose an analytical method for the construction of Hartree-Fock phase diagrams for the (fermion) Hubbard model and various generalizations thereof. Such phase diagrams are traditionally constructed numerically, but we argue that, by using asymptotic techniques, it is possible to obtain analytic formulas approximating the curves separating the different phases to very high accuracy. To illustrate the new method, we apply it to the two-dimensional Hubbard model on the square lattice at zero temperature. This yields formulas for the Hartree-Fock phase boundaries that agree with, but also improve on, earlier numerical results. In particular, our results provide the first rigorous proof of the existence of mixed phases in this model. |
| title | On the Hartree-Fock phase diagram for the two-dimensional Hubbard model |
| topic | Mathematical Physics Strongly Correlated Electrons 81T40, 45M05, 81V74, 82D03 |
| url | https://arxiv.org/abs/2512.20441 |