Fig. 5: \({{\mathcal{S}}}^{xx}(q,\omega )\) in the 1/3 magnetization plateau phase.

All results are obtained by DMRG-TDVP calculations for a system with length L = 120, and the color coding of \({{\mathcal{S}}}^{xx}(q,\omega )\) uses a piecewise function with a boundary value U₀ = 2. a–h Respectively correspond to the cases with H_z = 0.3,0.4,⋯,0.9,1.0. The dispersion lines, distinguished by colors and numerical labels, correspond to various localized excitations within a single trimer. (1)(2)(4) are the excitations from \(\left\vert 0\right\rangle \to \left\vert 1\right\rangle\), \(\left\vert 0\right\rangle \to \left\vert 3\right\rangle\) and \(\left\vert 0\right\rangle \to \left\vert 6\right\rangle\) with ΔM =− 1, respectively. (3) is the excitations from \(\left\vert 0\right\rangle \to \left\vert 4\right\rangle\) with ΔM = 1.