Fractional $S^z$ excitation and its bound state around the 1/3 plateau of the $S=1/2\mathrm{}$ Ising-like zigzag $\mathrm{XXZ}$ chain

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag $\mathrm{XXZ}$ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying $S^z=\pm 1/3$ and its bound state of $S^z=\pm 2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.