Revisiting a variational study of the quantum $J_1-J_1^{{}^{\mathrm{\prime }}}-J_2$ spin-1/2 Heisenberg antiferromagnet

The variational study of the ground state of the spin$-1\mathrm{/}2$ anisotropic Heisenberg antiferromagnet has been revisited on a square lattice by improving and correcting past numerical results found in Sol. State. Comm. 165, 33 (2013). The Hamiltonian has been implemented on a square lattice with antiferromagnetic interactions between nearest- and next-nearest neighbors. The nearest-neighbor couplings have different strengths, namely, $J_1$ and $J_1^{{}^{\mathrm{\prime }}}$, for the x and y directions, respectively. These couplings compete with the next-nearest ones denoted by $J_2$. We obtained a new phase diagram in the $\lambda -\alpha$ plane, where $\lambda =J_1^{{}^{\mathrm{\prime }}}\mathrm{/}{J}_1$ and $\alpha = J_{2}/J_{1}$, whose topology is slightly different of that previously found. There is no direct frontier dividing the collinear (CAF) and the antiferromagnetic order (AF), rather, the quantum paramagnetic phase (QP) separates these two phases for all positive values of $\lambda$ and $\alpha$. The true nature of the frontiers has been obtained by scanning rigorously the relevant points of the $\lambda -\alpha$ plane.