On the eigenstates of a Heisenberg chain with complex wavenumbers not forming strings

The nature of those S^z=0 excitations of an anisotropic Heisenberg chain that have been found to be typical in the low-energy excited states is considered. A simple estimation is used to take into account the effect of complex phase shifts on the long-distance decay properties of the wavefunction. It is established that pairs of complex wavenumbers that do not form two-strings correspond to pairs of free spins, while quartets described two independent pairs of bound spins.