Exact density matrix of the Gutzwiller wave function as the ground state of the inverse-square supersymmetrict−Jmodel

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-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 3k 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.

Exact density matrix of the Gutzwiller wave function as the ground state of the inverse-square supersymmetrict−Jmodel. II. Minority spin component

“…This discussion is almost identical to that in Ref. [11], but is reproduced here because it is essential to understanding the diagrammatic expansion. We make extensive use of a determinant representation of |Ψ G ({z})| 2 following ref.…”

“…As in Ref. [11], we refer to the boundary between magnon and hole momenta in B(M, Q) as the magnon-hole boundary, shown by a dashed line in Fig. 1, even though in a general diagram there can be magnon lines that go below this boundary and hole lines that go above this (for the holes that are the two jokers).…”

“…As explained in Ref. [11], each magnon line is either horizontal or exchanges partners with an adjacent magnon line to form a 'dimer'. As a result, the factor of (2 cos φ) M changes to F (M, Q), introduced in I. F (M, Q) describes the contribution of magnon pairs and dimers, and is defined by the recursion relation…”

“…In a previous paper [11], hereafter referred to as I, we adopted another approach, and derived the exact density matrix of the Gutzwiller wave function in a closed form. Our results in I, however, have been restricted to the majority-spin component.…”