Magnetic order in a spin-half interpolating square-triangle Heisenberg antiferromagnet

Using the coupled cluster method we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called $J_1$–$J_2^{\mathrm{\prime }}$ model, defined on an anisotropic 2D lattice. With respect to an underlying square-lattice geometry the model contains antiferromagnetic ($J_1>0$) bonds between nearest neighbors and competing ($J_2^{\mathrm{\prime }}>0$) bonds between next-nearest neighbors across only one of the diagonals of each square plaquette, the same diagonal in every square. Considered on an equivalent triangular-lattice geometry the model may be regarded as having two sorts of nearest-neighbor bonds, with $J_2^{\mathrm{\prime }}\equiv \kappa J_1$ bonds along parallel chains and $J_1$ bonds providing an interchain coupling. Hence, the model interpolates between a spin-half HAF on the square lattice at one extreme ($\kappa =0$) and a set of decoupled spin-half chains at the other ($\kappa \to \infty$),withthespin-halfHAFonthetriangularlatticeinbetweenat$\kappa = 1$. We find strong evidence that quantum fluctuations favor a first-order transition from quasiclassical N'{e}el order to a quantum helical state at a first critical point at ${\kappa }_{c_1}=0.80\pm 0.01$, by contrast with the corresponding second-order transition between the equivalent classical states at ${\kappa }_{\mathrm{c}\mathrm{l}}=0.5$. We also find strong evidence for a second critical point at ${\kappa }_{c_2}=1.8\pm 0.4$ where another first-order transition occurs, this time from the quantum helical phase to a collinear stripe-ordered phase. This latter result provides quantitative verification of a recent qualitative prediction of Starykh and Balents [Phys.
Rev. Lett. {\bf 98}, 077205 (2007)] for the $J_1$–$J_2^{\mathrm{\prime }}$ model that did not, however, evaluate the corresponding critical point.