Quantum antiferromagnetism in the d=3 Hubbard model --- a spin-fluctuation approach

TL;DR

This paper develops a self-consistent spin-fluctuation theory to analyze the Néel temperature and quantum corrections in the three-dimensional Hubbard model, bridging weak and strong coupling regimes with good agreement to known results.

Contribution

It introduces a novel spin-fluctuation approach using RPA for the Hubbard model, providing insights into quantum effects and magnetic properties across all interaction strengths.

Findings

Accurate T_N vs. U predictions across the entire U/t range.

Quantum spin-fluctuation corrections to sublattice magnetization.

Agreement with high-temperature series expansion in the strong coupling limit.

Abstract

A self-consistent spin-fluctuation theory is developed to obtain T_N vs. U for the half-filled Hubbard antiferromagnet in the whole U/t range. Good agreement is obtained in the strong coupling limit with the high-temperature series-expansion result for the equivalent Heisenberg model. Quantum, spin-fluctuation correction to the sublattice magnetization is also obtained for all U at the one-loop level. A spin picture is used throughout, and quantum effects are incorporated through transverse spin fluctuations, which are evaluated in the RPA using a new method.