Phase transitions in the spin-half model

Abstract

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and in this article we present an application of the CCM to the spin-half (Formula presented) quantum spin model with nearest- and next-nearest-neighbor interactions on the linear chain and the square lattice. We present results for ground-state expectation values of such quantities as the energy and the sublattice magnetization. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of (Formula presented) of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (Formula presented) 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 transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given by (Formula presented) and (Formula presented). © 1998 The American Physical Society.