Elementary excitations in the ordered phase of spin- 12 J1 – J2 model on square lattice

We use the recently proposed four-spin bond-operator technique (BOT) to discuss the spectral properties of a frustrated spin-$\frac{1}{2}$ ${J}₁$--${J}₂$ Heisenberg antiferromagnet on a square lattice at ${J}₂<0.4{J}₁$ (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 multimagnon bound states (e.g., the Higgs excitation) because separate bosons describe them in the 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 $\mathbf{k}=(\ensuremath{\pi},0)$. Thus, we do not support the conjecture that the continuum of excitations observed experimentally and numerically near $\mathbf{k}=(\ensuremath{\pi},0)$ 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 the spin-0 quasiparticles becomes long-lived, and its spectrum merges with the magnon spectrum in the majority of the Brillouin zone at ${J}₂\ensuremath{\approx}0.3{J}₁$. We predict also that the Higgs excitation and another spin-0 quasiparticle become long-lived around $\mathbf{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ at ${J}₂\ensuremath{\gtrsim}0.3{J}₁$ and produce sharp anomalies in the longitudinal DSF.