  By exploiting density-matrix renormalization group techniques, we investigate
the spin dynamics of a spin-1/2 one-dimensional J1-J2 XXZ model with competing
ferromagnetic J1 and antiferromagnetic J2 exchange couplings under applied
magnetic fields. Numerical results of spin excitation spectra show that in the
field-induced spin quadrupole regime, the longitudinal component has a gapless
mode and the transverse component has a gapped mode irrespective of the
exchange anisotropy. The excitation gap of the transverse spin excitation
increases as the exchange anisotropy increases over the XY-like and Ising-like
regions, demonstrating that two-magnon bound states are stabilized due to the
easy-axis anisotropy.
