  We demonstrate many-body multifractality of the Bose-Hubbard Hamiltonian's
ground state in Fock space, for arbitrary values of the interparticle
interaction. Generalized fractal dimensions unambiguously signal, even for
small system sizes, the emergence of a Mott insulator, that cannot, however, be
naively identified with a localized phase in Fock space. We show that the
scaling of the derivative of any generalized fractal dimension with respect to
the interaction strength encodes the critical point of the superfluid to Mott
insulator transition, and provides an efficient way to accurately estimate its
position. We further establish that the transition can be quantitatively
characterized by one single wavefunction amplitude from the exponentially large
Fock space.
