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arXiv · 2403.14768

Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling

E. Langmann·J. Lenells
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Abstract

We study the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter $t$ in the $x$- and $y$-directions and a possibly different hopping parameter $t_z$ in the $z$-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases $t_z=0$ and $t_z=t$, respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that $t=1$, we analyze how the N\'eel temperature and the antiferromagnetic mean field depend on the coupling parameter, $U$, and on the hopping parameter $t_z$. We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as $t_z \to 0$. It is found that the asymptotic formulas are qualitatively different for $t_z = 0$ (the two-dimensional case) and $t_z > 0$ (the case of nonzero hopping in the $z$-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit $t_z \to 0$ in which the three-dimensional model reduces to the two-dimensional model.

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BibTeXRIS

E. Langmann, J. Lenells. 2024-03-21. Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling. https://doi.org/10.1007/s10955-024-03390-w

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