Gaussian Effective Potential and Antiferromagnetism in the Hubbard Model

TL;DR

This paper demonstrates that the Gaussian Effective Potential (GEP) is an effective variational method for analyzing antiferromagnetism in the 2D Hubbard model, providing results close to Monte Carlo simulations.

Contribution

The paper derives the GEP for the 2D Hubbard model and shows it accurately predicts antiferromagnetic order, improving over RPA and aligning with Monte Carlo results.

Findings

GEP predicts antiferromagnetic order parameter accurately.

GEP results are closer to Monte Carlo than RPA.

Method can be extended to other magnetic systems.

Abstract

The Gaussian Effective Potential (GEP) is shown to be a useful variational tool for the study of the magnetic properties of strongly correlated electronic systems. The GEP is derived for a single band Hubbard model on a two-dimensional bi-partite square lattice in the strong coupling regime. At half-filling the antiferromagnetic order parameter emerges as the minimum of the effective potential with an accuracy which improves over RPA calculations and is very close to that achieved by Monte Carlo simulations. Extensions to other magnetic systems are discussed.