A dynamical mean-field theory study of Nagaoka ferromagnetism

TL;DR

This study uses dynamical mean-field theory with quantum Monte Carlo to analyze the stability and nature of Nagaoka ferromagnetism in the Hubbard model, revealing sensitivity to lattice hopping parameters and phase transition types.

Contribution

It provides a detailed DMFT analysis of Nagaoka ferromagnetism, highlighting the effects of next-nearest-neighbor hopping and phase transition characteristics, and benchmarks the slave-boson method.

Findings

Negative t' stabilizes ferromagnetism at higher doping.

Paramagnetic transition is first order at t'=-0.1t and second order at t'=0.

Ferromagnetism emerges from an incoherent metal near half-filling.

Abstract

We revisit Nagaoka ferromagnetism in the U=oo Hubbard model within the dynamical mean-field theory (DMFT) using the recently developed continuous time quantum Monte Carlo method as the impurity solver. The stability of Nagaoka ferromagnetism is studied as a function of the temperature, the doping level, and the next-nearest-neighbor lattice hopping t'. We found that the nature of the phase transition as well as the stability of the ferromagnetic state is very sensitive to the t' hopping. Negative t'=-0.1t stabilizes ferromagnetism up to higher doping levels. The paramagnetic state is reached through a first order phase transition. Alternatively, a second order phase transition is observed at t'=0. Very near half-filling, the coherence temperature T_{coh} of the paramagnetic metal becomes very low and ferromagnetism evolves out of an incoherent metal rather than conventional Fermi liquid. We use the DMFT results to benchmark slave-boson method which might be useful in more complicated geometries.