Dynamic properties of the dimerized spin-1/2 isotropic XY chain in a transverse field

The zz and xx (yy) dynamic structure factors of the dimerized spin-1/2 isotropic XY chain in a transverse (z) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.