Finite-temperature lineshapes in gapped quantum spin chains

We consider the finite-temperature dynamical susceptibility $\chi (\omega ,q,T)$ of gapped quantum spin chains such as the integer spin Heisenberg and transverse field Ising models. At zero temperature $\chi$ in these models is dominated by a delta-function line arising from the coherent propagation of single-particle modes. Using methods of integrable quantum field theory, we determine the evolution of the lineshape at low temperatures. We show that the lineshape is in general asymmetric in energy. We discuss the application of our results to inelastic neutron-scattering experiments on gapped spin chain systems such as ${\text{Y}}_2{\text{BaNiO}}_5$ and ${\text{CsNiCl}}_3$.

Figure 1

(Color online) Imaginary part of $\chi \left(\omega ,q\right)$ for several temperatures for the TFIM in the thermodynamic limit.

Figure 2

(Color online) Imaginary part of $\chi \left(\omega ,q\right)$ for several temperatures for the O(3) NLSM in the thermodynamic limit. Insets: temperature-dependent gap $\Delta \left(T\right)$ and width $\Gamma \left(T\right)$ (see text).