Nearest-neighbor correlations in the Hubbard model

Thomas Meintrup

Jakob Bernasconi

José A. Riera

We study the two-dimensional Hubbard model with next-nearest-neighbor hoppings and its related strong-coupling effective Hamiltonian by exact diagonalization. We found that the binding energy of holes tends to be smaller than with nearest neighbors only. However, the tendency towards phase separation is reduced by increasing the next-nearest-neighbor hopping. By studying pairing correlations, we found that the mode is strongly enhanced when the second-neighbor interactions are turned on.

Yu Shi

Pairing operators of electrons with an arbitrary distance on a square lattice are defined in each possible wave channel, s, p, ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$, ${\mathit{d}}_{\mathit{x}\mathit{y}}$, and ${\mathit{g}}_{\mathit{x}}^{3}$y-${\mathit{xy}}^{3}$. Exact identities among pairing amplitudes in the Hubbard model are presented, giving powerful constraints on the nature of pairings. At half filling, some of the pairing amplitudes, including those of the second-shortest pairing distance, vanish identically in each wave channel except the p wave. There are correlations among pairing amplitudes away from half filling, as well as nonidentically vanishing ones at half filling. Even if the pairing amplitudes vanish up to a certain distance, those of larger distances can still possibly be nonzero. The order of magnitude is estimated for the pairine amplitudes, indicating that those of large distances can by no means be neglected. The scheme is also used in the extended Hubbard model including nearest-neighbor density-density interaction and that including next-nearest-neighbor hopping. In that including nearest-neighbor interaction, the features of pairing amplitudes are just the same as in the original Hubbard model at half filling, and are also similar away from half filling, but with the difference that the amplitude is now dependent on the nearest-neighbor interaction. In the model including next-nearest-neighbor hopping, the features are quite different, the constraint identities are more underconstrained, and the amplitude has no monotonic dependence upon the pairing distance if the next-nearest-neighbor hopping has an opposite sign to the nearest-neighbor hopping as required physically. The same scheme is also used to discuss the possible pairings in the coupled two-plane Hubbard model and in the infinite-layer Hubbard model.

Jakob Bernasconi

Kazuo Saitoh, Satoshi Takada

The two-dimensional (2-D) Hubbard model with nearest-neighbor and next-nearest-neighbor (n.n.n.) hopping are studied using the Langevin method. Results of the staggered magnetic susceptibility and the pairing susceptibilities are shown. It is found that the effect of n.n.n. hopping destroys the antiferromagnetic correlation and assists the tendency of pairing. The possibility of superconductivity in the Hubbard model in the presence of n.n.n. hopping is discussed.