The breakdown of the mean-field description of the Nagaoka phase

TL;DR

This paper critically examines the limitations of the slave-fermion mean-field theory in describing the Nagaoka phase of the Hubbard model, revealing it predicts unrealistic ferromagnetic order and proposing a need for beyond mean-field approaches.

Contribution

The paper identifies the breakdown of the mean-field slave-fermion theory in accurately modeling the Nagaoka phase and discusses alternative low-energy effective spin actions.

Findings

Mean-field theory predicts long-range ferromagnetic order across all doping levels.

The slave-fermion mean-field approach does not accurately capture the Nagaoka phase physics.

A low-energy effective spin action is proposed to go beyond mean-field approximations.

Abstract

We discuss the relevance of the improved mean-field slave-fermion theory to describe the Nagaoka ($U=\infty$) limit of the Hubbard model. In this theory the crucial on-site constraint of no double electron occupancy is taken into account rigorously prior to the mean-field approximation. At one-loop approximation the effective mean-field action shows a long-range ferromagnetic order over the whole doping range. This indicates that the slave-fermion mean-field theory does not constitute an appropriate framework to describe the physics of the Nagaoka phase. We discuss the drawbacks of this mean-field theory and present some results on the derivation of a low-energy effective spin action to describe the Nagaoka phase beyond the mean-field approximation.