The Longitudinal Dynamic Correlation and Dynamic Susceptibility of the Isotropic Xy-model on the 1d Alternating Superlattice

The dynamic susceptibility χ Q (ω) of the isotropic XY-model (s=1/2) 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 < S jn(t)S z lm(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 χ Q (0), as a function of the transverse field h, and for the frequency dependency of the dynamic susceptibility χ Q (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, < ∑