Low-temperature asymptotic of the transverse dynamical structure factor for a magnetically polarized XX chain

The Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida–Tserkovnikov algorithm. Starting from this result a low-temperature integral representation for the corresponding magnon self-energy is obtained by the truncated form factor expansion, however, without any resummations. Within the suggested approach, the low-temperature asymptotics of the transverse dynamical structure factor may be readily studied. Some obtained line shapes are presented. (paper)