Let OK be a complete discrete valuation ring of mixed characteristic (0, p) with a perfect residue field. In this paper, for a semi-stable p-adic formal scheme X over OK with rigid generic fibre X and canonical log structureX , we study Hodge-Tate crystals over the absolute logarithmic prismatic site (X, M X ) ∆ . As an application, we give an equivalence between the category of rational Hodge-Tate crystals on the absolute logarithmic prismatic site (X, M X ) ∆ and the category of enhanced log Higgs bundles over X, which leads to an inverse Simpson functor from the latter to the category of generalised representations on X proét .