Dynamical mean-field theory study of Nagaoka ferromagnetism

Abstract

We revisit Nagaoka ferromagnetism in the $U=\ensuremath{\infty}$ 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 ${t}^{\ensuremath{'}}$. We found that the nature of the phase transition, as well as the stability of the ferromagnetic state, is very sensitive to the ${t}^{\ensuremath{'}}$ hopping. Negative ${t}^{\ensuremath{'}}=\ensuremath{-}0.1t$ 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 ${t}^{\ensuremath{'}}=0$. Very near half-filling, the coherence temperature ${T}_{\mathit{coh}}$ 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.