Excitation spectrum of planar spin-½ Heisenbergxxzchains

We present analytic weak-coupling and numerical finite-chain results for the dynamic form factor associated with the out-of-plane fluctuations at zero temperature and zero field. The dynamic form factor associated with the in-plane fluctuations is treated numerically only. In the ferromagnetic regime, the dominant features are traced back to particle-hole pair continua and the associated bound states. With the approach toward the isotropic ferromagnet, the resonance associated with the bound state of the particle-hole pairs gradually exhausts the spectrum, corresponding in this limit to the magnon peak. In the antiferromagnetic regime, the spectrum is dominated by the particle-hole pair continuum. The analytic results for the dynamic form factor associated with the out-of-plane fluctuations reproduce and extend the well-known properties of the continuum model to leading order in the coupling constant. As expected from the relation between the six-vertex model and the $\mathrm{xxz}$ chain, these properties include singular behavior of dynamic form factors depending continuously on the coupling constant.