Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor 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-neighbor exchange bonds $[J>\mathrm{}0\mathrm{}$ (antiferromagnetic) and $-\infty <J^{\prime }<\infty ]$ using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Néel 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 Néel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants $J^{\prime }>0.\mathrm{}$ For frustrating ferromagnetic couplings $J^{\prime }<0\mathrm{}$ we find indications that quantum fluctuations favor a first-order phase transition from the Néel 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 $J^{\prime }=0,$ which is equivalent to the honeycomb lattice, is treated more closely.