Breakdown of the Nagaoka phase at finite doping

TL;DR

This study uses quantum Monte Carlo simulations to analyze the Nagaoka phase in the Hubbard model at finite doping, finding no evidence of ferromagnetic correlations or ordering at finite temperature.

Contribution

It maps the Nagaoka limit of the Hubbard model onto a Kondo model and demonstrates the absence of ferromagnetic correlations at finite doping and temperature.

Findings

No short-range ferromagnetic correlations at doping ≥ 0.01

No indication of ferromagnetic ordering in the ground state

Simulations performed at finite temperature T=0.1t

Abstract

The Nagaoka ($U=\infty$) limit of the Hubbard model on a square lattice is mapped onto the itinerant-localized Kondo model at infinitely strong coupling. Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to compute spin correlation functions. This model is shown to exhibit no short-range ferromagnetic (FM) spin correlations at any doping $\delta\ge 0.01$ and finite temperature, $T=0.1t$. Our simulations give no indication that there is a tendency towards ferromagnetic ordering in the ground state.