Frustration of antiferromagnetism in the t-t'-Hubbard model at weak coupling

TL;DR

This paper investigates how next-nearest neighbor hopping t' suppresses antiferromagnetism in the Hubbard model at weak coupling, providing exact asymptotic behaviors and identifying a metallic antiferromagnetic phase in three dimensions.

Contribution

It offers the first exact asymptotic analysis of the critical coupling U_c(t') in various dimensions and clarifies the stability of metallic antiferromagnetic phases.

Findings

Suppression of antiferromagnetism by t' at weak coupling.

Exact asymptotic behavior of U_c(t') in 2D, 3D, and infinite dimensions.

Identification of a stable metallic antiferromagnetic phase in 3D.

Abstract

The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t'. The exact asymptotic behavior of the critical coupling U_c(t') at small t' is calculated in dimensions d=2,3 and infinity using Hartree theory, and the order of the transition is determined. A region of stability of a metallic antiferromagnetic phase in d=3 is identified.