Exact density matrix of the Gutzwiller wave function as the ground state of the inverse-square supersymmetric t−J model

Abstract

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 $1∕{r}^{2}$ 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 ${k}_{F}$ is identified. The form of the weaker singularity at $3{k}_{F}$ 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.