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Physica B Condensed Matter

Analytical diagonalization study of a two-orbital Hubbard model on a two-site molecule

Maria Emilia Amendola, Alfonso Romano, Canio Noce

Published Oct 17, 2015• 4 citations
Publisher
DOI
10.1016/j.physb.2015.10.003

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The two-orbital degenerate Hubbard model proves to be a powerful tool in the investigation of several 3 d and 4 d transition metal oxides where orbital degeneracy is known to play a crucial role. We present here a finite-size cluster study of this model where an exact numerical diagonalization procedure is used, based on the implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. The technique is then applied to the solution of the model on a four-site ring, and an explicit comparison is presented between the behavior of the spin, charge and orbital gaps as the on-site Coulomb repulsion is varied.

Journal of Physics Conference Series•Mar 1, 2009•0 citations
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction UUU at the ddd-orbital and the charge-transfer energy ΔΔΔ between the ddd- and ppp-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of UUU and ΔΔΔ. The analytic results are in good agreement with the numerical results of the exact diagonalization method.
Several recent exact-diagonalization calculations have established that the Anderson-Hubbard model has a disorder-induced zero bias anomaly (ZBA) (also called a disorder-induced pseudogap) in the density of states. In order to understand the physics of the ZBA, we study a simplified problem---an ensemble of two-site molecules with random site energies---for which analytical results are possible. For this ensemble, we examine how the ZBA forms in both the weakly correlated (mean field) and strongly correlated limits. In the weakly correlated case, the ZBA can be understood as the result of level repulsion between bonding and antibonding molecular orbitals. A similar level repulsion occurs in the strongly correlated case too but a larger contribution to the ZBA comes from the suppression of a triplet excitation mode. This inherently many-body mechanism does not have a counterpart in mean-field models.
The two-orbital degenerate Hubbard model proves to be a powerful tool in the investigation of several 3 d and 4 d transition metal oxides where orbital degeneracy is known to play a crucial role. We present here a finite-size cluster study of this model where an exact numerical diagonalization procedure is used, based on the implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. The technique is then applied to the solution of the model on a four-site ring, and an explicit comparison is presented between the behavior of the spin, charge and orbital gaps as the on-site Coulomb repulsion is varied.