  We study many-body localization in a hardcore boson model in the presence of
random disorder on finite generation fractal lattices with different Hausdorff
dimensions and different local lattice structures. In particular, we consider
the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal
lattices. In the single-particle case, these systems display Anderson
localization for arbitrary disorder strength if they are large enough. In the
many-body case, the systems available to exact diagonalization exhibit a
transition between a delocalized and localized regime, visible in the spectral
and entanglement properties of these systems. The position of this transition
depends on the Hausdorff dimension of the given fractal, as well as on its
local structure.
