  Assign to each vertex of the one-dimensional torus i.i.d. weights with a
heavy-tail of index $\tau-1>0$. Connect then each couple of vertices with
probability roughly proportional to the product of their weights and that
decays polynomially with exponent $\alpha>0$ in their distance. The resulting
graph is called scale-free percolation. The goal of this work is to study the
mixing time of the simple random walk on this structure. We depict a rich phase
diagram in $\alpha$ and $\tau$. In particular we prove that the presence of
hubs can speed up the mixing of the chain. We use different techniques for each
phase, the most interesting of which is a bootstrap procedure to reduce the
model from a phase where the degrees have bounded averages to a setting with
unbounded averages.
