On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature

Fuente: arXiv
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Main Authors: Langmann, Edwin, Lenells, Jonatan
Format: Preprint
Published: 2025
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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
id 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