On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911324586377216 |
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| author | Langmann, Edwin Lenells, Jonatan |
| author_facet | Langmann, Edwin Lenells, Jonatan |
| contents | We consider the antiferromagnetic gap for the half-filled two-dimensional (2D) Hubbard model (on a square lattice) at zero temperature in Hartree-Fock theory. It was conjectured by Hirsch in 1985 that this gap, $Δ$, vanishes like $\exp(-2π\sqrt{t/U})$ in the weak-coupling limit $U/t\downarrow 0$ ($U>0$ and $t>0$ are the usual Hubbard model parameters). We give a proof of this conjecture based on recent mathematical results about Hartree-Fock theory for the 2D Hubbard model. The key step is the exact computation of an integral involving the density of states of the 2D tight binding band relation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18141 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature Langmann, Edwin Lenells, Jonatan Mathematical Physics Strongly Correlated Electrons 81T25, 82D03, 45M05, 81V74 We consider the antiferromagnetic gap for the half-filled two-dimensional (2D) Hubbard model (on a square lattice) at zero temperature in Hartree-Fock theory. It was conjectured by Hirsch in 1985 that this gap, $Δ$, vanishes like $\exp(-2π\sqrt{t/U})$ in the weak-coupling limit $U/t\downarrow 0$ ($U>0$ and $t>0$ are the usual Hubbard model parameters). We give a proof of this conjecture based on recent mathematical results about Hartree-Fock theory for the 2D Hubbard model. The key step is the exact computation of an integral involving the density of states of the 2D tight binding band relation. |
| title | On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature |
| topic | Mathematical Physics Strongly Correlated Electrons 81T25, 82D03, 45M05, 81V74 |
| url | https://arxiv.org/abs/2501.18141 |