Elementary excitations in undoped layered cuprates

Using the recently proposed bond-operator technique (BOT), we discuss spin dynamics of the Heisenberg spin-$\frac12$ antiferromagnet with the ring exchange and small interactions between the second- and the third-neighbor spins on the square lattice at $T=0$. This model was suggested before for description of parent compounds of high-temperature superconducting layered cuprates. BOT describes accurately short-range spin correlations in quantum systems and provides a quantitative description of elementary excitations which appear in other approaches as bound states of conventional low-energy quasiparticles. We demonstrate that besides well-known magnons (spin-1 excitations) there are three well-defined spin-0 quasiparticles in the considered model whose energies lie near the magnon spectrum. Two of them, the amplitude (Higgs) mode and the quasiparticle which we named singlon, produce pronounced anomalies observed experimentally in the Raman scattering, resonant inelastic x-ray scattering, and infrared optical absorption. We find sets of the model parameters which describe quantitatively experimental data obtained in $\rm La_2CuO_4$ and $\rm Sr_2CuO_2Cl_2$.