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Journal of Physics F Metal Physics

One-dimensional Hubbard model with nearest and second nearest neighbour hopping in the Hartree-Fock approximation

E. Marsch, W.‐H. Steeb, D. Grensing

Published Mar 1, 1977• 6 citations
Publisher

Abstract

The Hubbard model is investigated within the Hartree-Fock approximation for the linear chain where nearest and second-nearest-neighbour hopping is taken into account.
DOI
10.1088/0305-4608/7/3/011

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Physical review. B, Condensed matter•Dec 1, 1988•1 citation
We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping far spin up (down) which depends on the total occupation n(b) of spin down (up) electrons on both sites involved. The hopping parameters are t(AA), t(AB) and t(BB) for n(b) = 0, 1, 2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t(AB) < t(AA) = t(BB) and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences.
Within the framework of the perturbation expansion of the linear-chain Hubbard model to fourth order in t/U, we consider the effect of second-neighbor interactions \ensuremath{\propto}(t/U)4{)}^{4})4 on the spin-Peierls transition temperature Tc{T}_{c}Tc​ in spin-1/2 Heisenberg chains. We find that the results can be interpreted in terms of a reduced ``effective'' nearest-neighbor antiferromagnetic exchange interaction when the spin-spin interactions are treated in the Hartree-Fock approximation. In the boson algebra approach, we show that this reduced interaction is of a different functional form than in the Hartree-Fock approach and is manifested in a decreased spin-wave velocity c. For typical couplings of the spins to the lattice, both approaches yield a spin-phonon interaction constant greater than the nearest-neighbor value of \ensuremath{\lambda}, but again with different functional forms and the Hartree-Fock Tc{T}_{c}Tc​ is raised by the second-neighbor interactions, by as much as 30% for \ensuremath{\lambda}=0.5 and (t/U)2{)}^{2})2\ensuremath{\simeq}0.1. This is discussed in the light of the fact that, in the Cross and Fisher approach, we find Tc{T}_{c}Tc​ to be independent of J2{J}_{2}J2​.