  We generate translationally invariant systems exhibiting many-body
localization from All-Bands- Flat single particle lattice Hamiltonians dressed
with suitable short-range many-body interactions. This phenomenon - dubbed
Many-Body Flatband Localization (MBFBL) - is based on symmetries of both single
particle and interaction terms in the Hamiltonian, and it holds for any
interaction strength. We propose a generator of MBFBL Hamiltonians which covers
both interacting bosons and fermions for arbitrary lattice dimensions, and we
provide explicit examples of MBFBL models in one and two lattice dimensions. We
also explicitly construct an extensive set of local integrals of motion for
MBFBL models. Our results can be further generalized to long-range interactions
as well as to systems lacking translational invariance.
