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The frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square latticehas been extensively studied since 1988 because of its close relationship tothe high-temperature superconductivity in cuprates and more importantlyinvolved novel phase of matter in its own right, namely, quantum spin liquid(QSL), one of hot topics in condensed matter physics in recent years. However,the phase diagram of the model, particularly in the maximally frustrated regime$J_2/J_1 \sim 0.5$, is quite controversial, and more seriously the nature ofthe QSL is not clear at all. Here we provide a pattern picture, on one hand, toshow explicitly how the system evolves from the N\'eel antiferromagnetic (AFM)state at small $J_2$ to the striped AFM one at large $J_2$; on the other hand,to uncover the nature of the QSL if it exists in the intermediate $J_2$coupling regime. For simplicity, we show our results by taking the squarelattice $L=L_x \times L_y$ with size $L_x=L_y=4$ here and periodic boundarycondition is considered, and furthermore, exact diagonalization is employed toconfirm the correctness of our picture. Our results indicate that the highlyfrustration regime is characterized by diagonal two-domain, while the N\'eelAFM state has a diagonal single-domain and the striped AFM state shows itselfas a diagonal four-domain, namely, completely diagonal antiferromagnetic order,in the present case. Increasing the system size, the number of the diagonaldomains increases correspondingly, but the diagonal single-domain for theN\'eel AFM state and the diagonal $L_{x(y)}$-domain for the striped AFM stateremain unchanged. Our results shed light on the understanding of the QSL.

An explicit evolution from N\'eel to striped antiferromagnetic states in the spin-1/2 $J_{1}$-$J_{2}$ Heisenberg model on the square lattice