Quantum Phase Transitions of a Square-Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled-Cluster Treatment

We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spin-half Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J>0 (antiferromagnetic) and J'>0, J'<0) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Neel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Neel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants J'>0. For frustrating ferromagnetic couplings J'<0 we find indications that quantum fluctuations favour a first-order phase transition from the Neel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J'=0, which is equivalent to the honeycomb lattice, is treated more closely.