Phase Transitions in the Spin-Half J_1--J_2 Model

TL;DR

This paper applies the coupled cluster method to the spin-half J_1--J_2 model, analyzing phase transitions, critical points, and the breakdown of the Marshall-Peierls sign rule on linear chains and square lattices.

Contribution

It provides new CCM-based results for ground-state properties and identifies critical points and sign rule breakdowns in the J_1--J_2 model, linking wave function coefficients to correlation functions.

Findings

Critical point at J_2/J_1 = 0.26 for sign rule breakdown

Critical point at J_2/J_1 = 0.61 for phase transition

Ground-state energy and magnetization estimates

Abstract

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. 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 J_2/J_1, of the Marshall-Peierls sign rule which 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 transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.