2010/12/02 by Andrzejewski, Lukasz, Jedrzejewski, Janusz
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1012.0443
We consider nearly-flat-band Hubbard models of a ferromagnet, that is the models that are weak perturbations of those flat-band Hubbard models whose ground state is ferromagnetic for any nonzero strength U of the Hubbard repulsion. In contrast to the flat-band case, in the nearly-flat-band case the ground state, being paramagnetic for U in a vicinity of zero, turns into a ferromagnetic one only if U exceeds some nonzero threshold value Uth. We address the question whether Uth of the considered models is in a physical range, therefore we attempt at obtaining possibly good estimates of the threshold value Uth. A rigorous method proposed by Tasaki is extended and the resulting estimates are compared with small-system, finite-size scaling results obtained for open- and periodic-boundary conditions. Contrary to suggestions in literature, we find the latter conditions particularly useful for our task.