The density matrix, i.e., the Fourier transform of the momentum distribution, is obtained analytically for all values of the magnetization of the Gutzwiller wave function in one dimension with the exclusion of double occupancy per site. The present result complements the previous analytic derivation of the density matrix for the majority spin. The derivation makes use of a determinantal form of the squared wave function, and multiple integrals over particle coordinates are performed with the help of a diagrammatic representation. In the thermodynamic limit, the density matrix at distance
x is completely characterized by quantities
vcx and
vsx, where
vs and
vc are spin and charge velocities in the supersymmetric $t\text{\ensuremath{-}}J$ model for which the Gutzwiller wave function gives the exact ground state. The present result then gives the exact density matrix of the $t\text{\ensuremath{-}}J$ model for all densities and all magnetization at zero temperature. Discontinuity, slope, and curvature singularities in the momentum distribution are identified. The momentum distribution obtained by numerical Fourier transform is in excellent agreement with existing results.
The density matrix---i.e., the Fourier transform of the momentum distribution---is obtained analytically in closed form for the Gutzwiller wave function with exclusion of double occupancy per site. The density matrix for the majority spin is obtained for all magnetizations including the singlet case. Since the wave function gives the ground state of the supersymmetric $t\text{\ensuremath{-}}J$ model with the
1∕r2 exchange and transfer, the result gives the exact density matrix of the model at zero temperature. From the oscillating behavior of the density matrix, the discontinuity of the momentum distribution at the Fermi momentum
kF is identified. The form of the weaker singularity at
3kF is also obtained; there is a discontinuity in the second derivative of the momentum distribution, whose magnitude is calculated analytically. The momentum distribution over the whole Brillouin zone is obtained numerically from the analytic solution of the density matrix. The result is in excellent agreement with previous results derived by different methods.
Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.