P-adic non abelian Hodge theory, also known as the p-adic Simpson correspondence, aims at describing p-adic local systems on a smooth rigid analytic variety in terms of Higgs bundles. I will explain in this talk why the « Hodge-Tate stacks » recently introduced by Bhatt-Lurie and Drinfeld in their work on prismatic cohomology can be useful to study this kind of questions. Joint work with Johannes Anschütz and Ben Heuer.