The longitudinal dynamic correlation and dynamic susceptibility of the isotropic XY-model on the 1d alternating superlattice
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The dynamic susceptibility $χ_{Q}^{zz}(ω)$ 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 $<S_{jn}^{z}(t)S_{lm}^{z}(0)>$, 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 $χ_{Q}^{zz}(0)$, as a function of the transverse field h, and for the frequency dependency of the dynamic susceptibility $χ_{Q}^{zz}(ω)$. 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, $<\sum\limits_{n;m\in cell:\text{}j;l}S_{jn}^{z}(t)S_{lm}^{z}(0)>$, is time independent, which constitutes an unexpected result.
14 pages, 13 figures, preliminary version presented at STATPHYS21, submitted to Physica A
14 pages, 13 figures, preliminary version presented at STATPHYS21, submitted to Physica A