Spectral density approach for the damping of fermion elementary excitations in an anisotropic spin-12 linear chain

The paper is devoted to an investigation of the damping effects of the Fermion elementary excitations in the Jordan-Wigner representation of a one-dimensional anisotropic spin-12 model in an external field. This is realized on the basis of the “Gaussian ansatz”, recently proposed by Nolting and Oles, as substituting the standard “polar ansatz” in the Spectral Density Method, for exploring damping effects of quasi-particles in many-body problems. By using a first order approximation, we are able to obtain reasonable results in the low temperature limit.