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

Abstract

The dynamic susceptibility ${\chi }_Q^{zz}(\omega )$ 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 $<S_{jn}^z(t)S_{lm}^z(0)>$, 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 ${\chi }_Q^{zz}(0)$, as a function of the transverse field h, and for the frequency dependency of the dynamic susceptibility ${\chi }_Q^{zz}(\omega )$. 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, $<\sum _{n;m\in cell:j;l}{S}_{jn}^z(t)S_{lm}^z(0)>$, is time independent, which constitutes an unexpected result.

14 pages, 13 figures, preliminary version presented at STATPHYS21, submitted to Physica A