ANALYSIS OF THE GROUND-STATE WAVE-FUNCTION OF THE J1-J2 QUANTUM HEISENBERG-ANTIFERROMAGNET

We investigate the ground-state wave function \psi] = SIGMA(n) alpha(n)\n] of the spin 1/2 J1 - J2 model on finite square lattices of N = 16 (4 x 4) and N = 24 (4 x 6) sites. We find that the Marshall-Peierls phase rule for coefficients alpha(n), which was derived for unfrustrated bipartite lattices (J2 = 0), holds exactly for comparably large frustration up to J2/J1 = 0.28 (N = 16) and up to J2/J1 = 0.20 (N = 24). But even for strong frustration up to J2/J1 almost-equal-to 0.45 the Marshall-Peierls rule describes the phase relationships in the ground state excellently. In the region of dominating J2 a phase rule can be formulated as a product of the rules for two independent antiferromagnets. We find that the violation of the Marshall-Peierls sign rule does not dramatically affect the order parameters UP to J2/J1 almost-equal-to 0.6. To calculate the magnitude of the coefficients alpha(n) by a variational procedure we search for a represantative relationship between the alpha(n) and (a few) parameters P1,n...P(k,n) classifying the Ising basis states \n]. By comparison with the exact ground state we analyze classification schemes based on pair correlations (Jastrow type wave functions) as well as schemes taking into account cluster parameters. While for small frustration J2/J1 < 0.2 a short-range Jastrow description (nearest-neighbour and next nearest-neighbour pairing) seems to be sufficient for the adequate description of the ground state one definitly needs long-range pairing and/or cluster parameters to construct a reasonable trial wave function for strong frustration. As an example for a special Jastrow type wave function we discuss an ansatz coming from the spin-wave theory. Finally, we consider the influence of the anisotropic exchange J(zz) not-equal J(xx), J(yy) on the quality of the short-range Jastrow wave function and find an excellent agreement with the exact ground state already for Ising exchange anisotropies J(xx) = J(yy) almost-equal-to 0.5 J(zz).