PHASE-TRANSITIONS IN THE SPIN-HALF J(1)-J(2) MODEL

The coupled cluster method (CCM) is a well-known method of quantum man y-body theory, and in this article we present an application of the CC M to the spin-half J(1)-J(2) quantum spin model with nearest- and next -nearest-neighbor interactions on the linear chain and the square latt ice. We present results for ground-state expectation values of such qu antities as the energy and the sublattice magnetization. The presence of critical points in the solution of the CCM equations, which are ass ociated with phase transitions in the real system, is investigated. Co mpletely distinct from the investigation of the critical points, we al so make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correla tion coefficients. We are thus able to present evidence of the breakdo wn, at a given value of J(2)/J(1), of the Marshall-Peierls sign rule w hich is known to be satisfied at the pure Heisenberg point (J(2)=0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase t ransition from the antiferromagnetic phase to the frustrated phase occ urs are, respectively, given by J(2)/J(1) approximate to 0.26 and J(2) /J(1) approximate to 0.61.