NAGAOKA FERROMAGNETISM AS A TEST OF SLAVE-FERMION AND SLAVE-BOSON APPROACHES

Abstract

The ferromagnetic to paramagnetic transition in the Nagaoka (U=∞) limit of the Hubbard Hamiltonian is used to test the applicability of slave-boson and slave-fermion (Schwinger boson) functional-integral approaches. Within the slave-fermion formalism to one-loop order, the ferromagnetic phase is stable to spin-wave, gauge field, and longitudinal fluctuations over a doping interval that is much too large compared with other approaches. Furthermore, nonbipartite lattices such as hcp or fcc lattices are ferromagnetic for t>0 over a wider doping interval than for t<0, in qualitative disagreement with all other types of calculations. It is possible to remedy all these defects in order to reach agreement, at least qualitatively, with previous studies. It suffices to take the point of view that in the U=∞ limit it is best to represent the paramagnetic phase as the mean-field solution of the slave-boson representation, and the ferromagnetic phase as the mean-field solution of the slave-fermion representation. The transition between both phases is taken to occur at the critical hole doping where the ground state energies are equal. This seems to give the best possible comparison with other approaches, despite the lack of a variational principle justifying comparisons of energies between slave-fermion and slave-boson representations. On bipartite lattices, the critical hole density found analytically by this procedure, δc=1/3, is identical to the critical density obtained in the Kotliar-Ruckenstein slave-boson approach. This value of δc is also close to various other estimates. Nevertheless, non-bipartite lattices with t>0 remain ferromagnetic over a small but finite doping interval, in quantitative disagreement with some other approaches.