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.
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=
kF is analyzed from the system size dependence. In addition to the
kF singularity, n(k) has a weak singularity at k=3
kF; however, no detectable singularity is present at 2
kF, which one might expect from the spinless fermion wave function. The singularity of S(k) at 2
kF 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
kF 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.
The momentum distribution function and spin-correlation functions are studied for the one-dimensional large-U Hubbard model with an emphasis on the effects of the magnetic field. A direct calculation of the correlation functions is carried out with the exact wave function, whose explicit form for the large-U limit was derived in a previous paper. Singularities are detected at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$+2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ in the momentum distribution function ${\mathit{n}}_{\mathrm{\ensuremath{\sigma}}}$(k), where ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ is the Fermi wave number of the noninteracting electrons with a given magnetization. Similarly, the longitudinal spin-correlation function
Szz(k) has singularities at 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$ and 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$, while the transverse one
Sxx(k) is singular at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$. The nature of the singularities (i.e., critical exponents) is determined from an analysis of the size dependence. As a complementary approach, those critical exponents for the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit are explicitly calculated with conformal field theory. In this limit the exponents depend only on the magnetization and are independent of the electron density. The resulting exponents are consistent with the first results.
We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.
The critical exponents for the charge, spin, electron, and superconducting correlation functions of the one-dimensional t-J model at t=J are obtained for arbitrary band filling. Our method is based on the Bethe-ansatz solution and the finite-size scaling analysis in conformal field theory. The long-distance behavior of the model belongs to the same universality class as the repulsive Hubbard model. Near half-filling the exponents take the values expected in the strong-correlation limit of the Hubbard model. In the low-density limit the exponents are those of the noninteracting system.