Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model

Abstract

The momentum distribution function n(k) and spin-correlation function S(k) are determined for the one-dimensional large-U Hubbard model with various electron densities. The present work is featured with an application of the Bethe-ansatz wave function, which has a simple form in the large-U limit for any electron density. Namely, its charge degrees of freedom are expressed as a Slater determinant of spinless fermions, while its spin degrees of freedom are equivalent to the one-dimensional S=(1/2 Heisenberg model. The singularity of n(k) at k=$k_F$ is analyzed from the system size dependence. In addition to the $k_F$ singularity, n(k) has a weak singularity at k=3$k_F$; however, no detectable singularity is present at 2$k_F$, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2$k_F$ is also examined in detail. It is concluded from the size dependence that, when the system is away from half-filling, the nature of the singularity at 2$k_F$ is different from that in the Heisenberg model. The results are compared with the behavior in the weak-correlation regime examined with the perturbation calculation, the prediction of g-ology, and recent Monte Carlo calculations.