Correlation Functions in One-Dimensional Large-U Hubbard Model : Zero-Field and Finite-Field Cases

N. M. Bogoliubov, V. E. Korepin

Hiroyuki Shiba, Masao Ogata

A recent study of the large-U limit of the one-dimensional (1D) Hubbard model is presented and discussed. It is pointed out first that the wave function has a simple structure in this limit. Namely, it is a product of Slater determinant of noninteracting spinless fermions and the wave function of 1D S=1/2 Heisenberg antiferromagnet. Secondly, by using this property, a direct calculation of momentum distribution and spin correlation function is carried out for the ground state at zero-field and finite-field cases. The results show various singularities exactly at the same position where one expects for the small-U case in both zero-field and finite-field cases. The critical exponents estimated from the size dependence are in reasonable agreement with those predicted by the Tomonaga-Luttinger-liquid and the conformal field theory.

D. M. Esterling

A companion paper derived exact relations for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension and any lattice structure. These relations involve moments of the spectral weight function but differ from earlier work by (a) restricting the moments over the interesting low energy (lower Hubbard band) spectrum and (b) without any of the usual approximations (e.g. decoupling) for the requisite higher order correlation functions. The latter are determined exactly as explicit functions of the single particle equal time correlation function in the infinite U limit. Here the relations offer rich insights into the model behavior and offer exacting tests - a computer lab - of any proposed solution to the Hubbard model in the strong correlation (large finite U) region. Specific tests are applied to mean field theory solutions to the Hubbard model as well as some one dimensional results. In each case, substantial problems are exposed. The relations are also used to determine a best(moment-preserving) solution subject only to the one assumption of a dominant single peak in the lower Hubbard band spectral weight function. As shown in the companion paper, the second central moment of the lower Hubbard band spectral weight function is not zero, as might be expected, as the electron density approaches one electron per site (paramagnetic case). That moment is large, offering a significant test for any approximate solution.

A. M. Finkel'Shteǐn

Yong Ren, P. W. Anderson

The one-dimensional Hubbard model with repulsive interaction is studied. We calculate the asymptotic correlation functions in the less-than-half-filled band case. In particular, our approach centers on the large-U wave function and emphasizes the finite phase shifts on the Fermi surface. This is important since the concept of finite phase shifts can be easily applied to higher dimensions. We then discuss the non-Fermi-liquid behavior of this model and the relevance to the understanding of the two-dimensional Hubbard model, which is believed to give a good description of the high-${\mathit{T}}_{\mathit{c}}$ superconductors.

J. M. P. Carmelo, D. Baeriswyl