Magnetism of the Single-Band Hubbard Model in the Strong Correlation Limit

K. Kubo
2013 Progress of Theoretical Physics Supplement  
The wave-vector dependence of the magnetic susceptibility of the singleband Huddard model is calculated by means of the high temperature expansion in the strong correlation limit (U = oo). The transition temperatures are estimated from the inverse susceptibility evaluated up to (fit)'. The ferromagnetic transition appears only in nearly half-filled triangular, bee and fcc lattices, but not in square and sc lattices. The various magnetic structures are suggested to be possible if the electron
more » ... sity is varied. § I. Introduction The single band Hubbard model is often adopted as a model Hamiltonian for itinerant ferromagnetism_v~•> In spite of its simplicity and much investigation it is still not well understood under which conditions the model shows ferromagnetism. Correlation effects make the competition between ferro-and paramagnetic states quite tight. In addition, one must take into account of possibilities of other types of magnetic phases, i.e., antiferromagnetism or spin density waves. The parameters coming into our discussions are electron number density n (n = Ne/ NL), the strength of the intraatomic Coulomb interaction U, the energy band parameters and the temperature T. The following discussions are restricted to the energy bands with only nearest neighbor hopping t, which is assumed to be positive without loss of generality. A phase diagram of the ground state was obtained by Penn for sc lattice. 5 > Although the ferromagnetic ground state was obtained for rather wide range of n, his results may not be justified in strongly correlated case because of Hartree-Fock approximation. In the strong correlation limit the ground states of the systems with Ne = NL -1 were rigorously proved to be ferromagnetic. 6 > The problem is still open in the case of macroscopic deviations from the halffilled lattice. The fcc lattice was studied by Plischke for arbitrary electron density. 7 > Finite Curie temperature was obtained for 1.2 from the high temperature expansion of the susceptibility up to ((3t) 9 • We also calculated the fourth order term in a previous paper (hereafter refered as I) . 8 > *> In his paper 0.2;:Sn;:S0.8, as he assumed t<O.
doi:10.1143/ptp.69.290 fatcat:srvkikci6ffldnlwiawzwkq5ze