Excitations in One-Dimensional $S=\frac{1}{2}$ Quantum Antiferromagnets

The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations. The spectral weights in the $S=1$ channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped, or doped quantum antiferromagnets.

Figure 1

Relative spectral weights $I_{\mathrm{n}\mathrm{,}\mathrm{r}\mathrm{e}\mathrm{l}}(\lambda )$ of the dynamic structure factor in the dimerized chain. Depicted are biased approximants with singularity at $\lambda =1$ and exponent $1/3$ for $I_{\mathrm{1}\mathrm{,}\mathrm{r}\mathrm{e}\mathrm{l}}$ ($[4,2]$, black solid line); exponent $-2/3$ in the derivative of $I_{\mathrm{2}\mathrm{,}\mathrm{r}\mathrm{e}\mathrm{l}}$ ($[3,2]$, dashed line) and similarly for $1000\times I_{\mathrm{3}\mathrm{,}\mathrm{r}\mathrm{e}\mathrm{l}}$ ([2,2], dash-dotted line). The solid line toward the top is the sum $\sum _{n=1}^3{I}_{\mathrm{n}\mathrm{,}\mathrm{r}\mathrm{e}\mathrm{l}}$.