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We study the phase diagram and the dynamical spin structure factor of thespin-1/2 J1-J3 Heisenberg model on the square lattice using density matrixrenormalization group, exact diagonalization (ED), and cluster perturbationtheory (CPT). By extrapolating the order parameters and studying the levelcrossings of the low-lying energy and entanglement spectra, we obtain the phasediagram of this model and identify a narrow region of quantum spin liquid (QSL)phase followed by a plaquette valence-bond solid (PVBS) state in theintermediate region, whose nature has been controversial for many years. Moreimportantly, we use CPT and ED to study the dynamical spin structure factor inthe QSL and the PVBS phase. In the QSL phase, the high-energy magnon modecompletely turns into some dispersive weak excitations around the X and Mpoints. For the PVBS phase, the low-energy spectrum is characterized by agapped triplet excitation, and at the high energy, we find another branch ofdispersive excitation with broad continua, which is unlike the plaquette phasein the 2x2 checkerboard model. In the latter case, the second branch ofexcitation is nearly flat due to the weak effective interactions between thelocal excitations of the plaquettes. And in the J1-J3 Heisenberg model, theuniform interactions and the spontaneously translational symmetry breaking ofthe PVBS phase make the difference in the excitation spectra.

Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice