  We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the
energy-resolved correlation between spectral features and structural changes of
the associated eigenstates as exposed by their generalized fractal dimensions.
The eigenvectors are shown to become ergodic in the thermodynamic limit, in the
configuration space Fock basis, in which random matrix theory offers a
remarkable description of their typical structure. The distributions of the
generalized fractal dimensions, however, are ever more distinguishable from
random matrix theory as the Hilbert space dimension grows.
