The longitudinal dynamic correlation and dynamic susceptibility of the isotropic XY-model on the 1D alternating superlattice

The dynamic susceptibility χQzz(ω) of the isotropic XY-model (s=12) on the alternating superlattice (closed chain) in a transverse field h is obtained exactly at arbitrary temperatures. It is determined from the results obtained for the dynamic correlations 〈Sj,nz(t)Sl,mz(0)〉, which have been calculated by introducing the generalized Jordan–Wigner transformation, by using Wick's theorem and by reducing the problem to a diagonalization of a finite matrix. The static properties are also reobtained within this new formalism and all exact results are determined for arbitrary temperatures. Explicit results are obtained numerically in the limit T=0, where the critical behaviour occurs. A detailed analysis is presented for the behaviour of the static susceptibility χQzz(0), as a function of the transverse field h, and for the frequency dependency of the dynamic susceptibility χQzz(ω). It is also shown, in this temperature limit, that within the magnetization plateaus which correspond to the different phases, even when the induced magnetization is not saturated, the effective dynamic correlation, 〈∑n;m∈cell:j;lSj,nz(t)Sl,mz(0)〉, is time independent, which constitutes an unexpected result.