Elementary excitations in the ordered phase of spin-1/2 J1-J2 model on square lattice

We use recently proposed four-spin bond-operator technique (BOT) to discuss spectral properties of frustrated spin-$\frac12$ $J_1$--$J_2$ Heisenberg antiferromagnet on square lattice at $J_2<0.4J_1$ (i.e., in the N\'eel ordered phase). This formalism is convenient for the consideration of low-lying excitations which appear in conventional approaches as multi-magnon bound states (e.g., the Higgs excitation) because separate bosons describe them in BOT. At $J_2=0$, the obtained magnon spectrum describes accurately available experimental data. However, calculated one-magnon spectral weights and the transverse dynamical structure factor (DSF) do not reproduce experimental findings quantitatively around the momentum ${\bf k}=(\pi,0)$. Then, we do not support the conjecture that the continuum of excitations observed experimentally and numerically near ${\bf k}=(\pi,0)$ is of the Higgs-magnon origin. Upon $J_2$ increasing, one-magnon spectral weights decrease and spectra of high-energy spin-0 and spin-1 excitations move down. One of spin-0 quasiparticles becomes long-lived and its spectrum merges with the magnon spectrum in the most part of the Brillouin zone at $J_2\approx0.3J_1$. We predict that the Higgs excitation and another spin-0 quasiparticle become long-lived around ${\bf k}=(\pi/2,\pi/2)$ at $J_2\agt0.3J_1$ and produce sharp anomalies in the longitudinal DSF.