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The variational study of the ground state of the spin$-1/2$ anisotropicHeisenberg antiferromagnet has been revisited on a square lattice by improvingand correcting past numerical results found in Sol. State. Comm. 165, 33(2013). The Hamiltonian has been implemented on a square lattice withantiferromagnetic interactions between nearest- and next-nearest neighbors. Thenearest-neighbor couplings have different strengths, namely, $J_{1}$ and$J_{1}^{'}$, for the x and y directions, respectively. These couplings competewith the next-nearest ones denoted by $J_{2}$. We obtained a new phase diagramin the $\lambda - \alpha$ plane, where $\lambda= J_{1}^{'}/J_{1}$ 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 theantiferromagnetic 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 therelevant points of the $\lambda-\alpha$ plane.

Revisiting a variational study of the quantum $J_{1}-J_{1}^{'}-J_{2}$ spin-1/2 Heisenberg antiferromagnet