Abstract 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, $\Delta$ Δ , vanishes like $\exp (-2\pi \sqrt{t/U})$ exp ( - 2 π t / U ) in the weak-coupling limit $U/t\downarrow 0$ U / t ↓ 0 ( $U>0$ U > 0 and $t>0$ 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.Abstract 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, $$\Delta $$ Δ , vanishes like $$\exp (-2\pi \sqrt{t/U})$$ exp ( - 2 π t / U ) in the weak-coupling limit $$U/t\downarrow 0$$ U / t ↓ 0 ( $$U>0$$ U > 0 and $$t>0$$ 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.

arXiv:2501.18141Letters in Mathematical PhysicsApr 20, 20260 citations

Antiferromagnetic state in the three-band Hubbard model

Tetsuro Asahata, Akira Oguri, Sadamichi Maekawa

Physica C SuperconductivityDec 1, 19941 citation

Variational cluster approach to the Hubbard model on a honeycomb lattice

Kazuhiro Seki, Y. Ohta

We study the ground-state properties of the Hubbard model on the honeycomb lattice at half filling. Using the variational cluster approximation, We study the semimetal-insulator transition and antiferromagnetism as functions of the on-site Coulomb interaction U . When U is switched on, a small, but finite, single-particle gap appears; thus, we conclude that a tiny gap appears with arbitrary small U > 0. With further increases in U , the system goes into the antiferromagnetic state. We find that the staggered magnetization increases continuously with increasing U and that the antiferromagnetic phase transition is of the second order.We study the ground-state properties of the Hubbard model on the honeycomb lattice at half filling. Using the variational cluster approximation, We study the semimetal-insulator transition and antiferromagnetism as functions of the on-site Coulomb interaction U . When U is switched on, a small, but finite, single-particle gap appears; thus, we conclude that a tiny gap appears with arbitrary small U > 0. With further increases in U , the system goes into the antiferromagnetic state. We find that the staggered magnetization increases continuously with increasing U and that the antiferromagnetic phase transition is of the second order.

Journal of the Korean Physical SocietyJun 1, 20134 citations

Enhancement of long-range antiferromagnetic order by nonmagnetic impurities in the Hubbard model

M. Ulmke, P. J. H. Denteneer, Richard T. Scalettar +1 more

The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P ( U i ) = (1 − f )δ( U i − U ) + f δ( U i ), is studied using finite-temperature Quantum Monte Carlo and dynamical mean-field theory. Long-range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U = 0 sites. Whereas in the clean model there is a single gap at n = 1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.The two-dimensional Hubbard model with a bimodal distribution of on-site interactions, P ( U i ) = (1 − f )δ( U i − U ) + f δ( U i ), is studied using finite-temperature Quantum Monte Carlo and dynamical mean-field theory. Long-range antiferromagnetic order off half-filling is stabilized by the disorder, due to localization of the dopants on the U = 0 sites. Whereas in the clean model there is a single gap at n = 1, for nonzero f we find the compressibility and density of states exhibit gaps at two separate fillings.

arXiv:cond-mat/9707068Europhysics Letters (EPL)Jun 15, 199813 citations

On the onset of antiferromagnetism in the Hubbard model

F. Ducastelle

Physics Letters ADec 1, 19774 citations

\Delta

Δ , vanishes like

\exp (-2\pi \sqrt{t/U})

exp ( - 2 π t / U ) in the weak-coupling limit

U/t\downarrow 0

U / t ↓ 0 (

U>0

U > 0 and

t>0

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.