Jonatan Lenells: Universality of mean-field antiferromagnetic order in an anisotropic Hubbard model

Abstract:

The Hubbard model is often described as being of similar importance to the quantum statistical mechanics of interacting fermions as the Ising model is to classical statistical mechanics. I will describe joint work with Edwin Langmann where we study the Hubbard model 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. We derive asymptotic formulas for the density of states, the Néel temperature, and the antiferromagnetic mean field. In particular, we show that the antiferromagnetic mean field has certain universality features for \(t_z > 0\) which are lost in the limit \(t_z \to 0\) where the three-dimensional model reduces to the two-dimensional model. Our results suggest that the anisotropic 3D Hubbard model with a small but nonzero value of \(t_z\) in some circumstances can serve as a more robust model for high-temperature superconductivity than the 2D Hubbard model.

Paper reference: arXiv:2403.14768 .