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Journal of Magnetism and Magnetic Materials

Magnetic response and fractional statistics in the infinite-range Hubbard model

Carlindo Vitoriano, Lucian Bogdan Bejan, A. M. S. Macêdo, Mauricio D. Coutinho-Filho

Published May 1, 2001• 2 citations
Publisher
DOI
10.1016/s0304-8853(00)00910-0

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We show that the Hubbard model with infinite-range Coulomb coupling is equivalent to an ideal gas of three species of particles obeying fractional exclusion statistics. A full appreciation of this mapping requires an extension of the pertinent formalism. This very simple, but rather peculiar model is exactly solvable in any dimension and exhibits a Mott metal-insulator transition, whose universality class is shown to be that of a free spinless Fermi gas. A modified version of the Luttinger theorem is shown to apply in any dimension. We also characterize the metallic and insulating phases by obtaining the electronic band structure as well as the interacting density of states. The fractional statistics manifests itself on the amplitudes of several thermodynamic quantities and, in particular, the Pauli spin susceptibility is subdominant in all metallic phases, and a Curie-type of response appears.
The ground state and low-temperature properties of the Hubbard model with infinite-range attractive interaction in the presence of a magnetic field are considered. This model is exactly solvable in any dimension and is mapped onto an ideal gas of three species of exclusons. The system is found to behave as a noninteracting Fermi gas whenever the correlation function $C(\mathbf{k})=⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩\ensuremath{-}⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}⟩⟨{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩$ is negligible, otherwise it displays nontrivial correlated behavior which manifests as fractional statistical effects. The corresponding effective Hamiltonians and free energies governing the distinct regimes are presented. In one dimension, our results are analyzed in light of those derived using the on-site attractive Hubbard chain.