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

The frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice has been extensively studied since 1988 because of its close relationship to the high-temperature superconductivity in cuprates and more importantly involved 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 of the QSL is not clear at all. Here we provide a pattern picture, on one hand, to show 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 square lattice $L=L_x \times L_y$ with size $L_x=L_y=4$ here and periodic boundary condition is considered, and furthermore, exact diagonalization is employed to confirm the correctness of our picture. Our results indicate that the highly frustration regime is characterized by diagonal two-domain, while the N\'eel AFM state has a diagonal single-domain and the striped AFM state shows itself as a diagonal four-domain, namely, completely diagonal antiferromagnetic order, in the present case. Increasing the system size, the number of the diagonal domains increases correspondingly, but the diagonal single-domain for the N\'eel AFM state and the diagonal $L_{x(y)}$-domain for the striped AFM state remain unchanged. Our results shed light on the understanding of the QSL.Comment: 6 pages, 4 figure