  We analytically study spectral correlations and many body wave functions of
an SYK-model deformed by a one body contribution to the Hamiltonian. Our main
result is the identification of a wide range of intermediate coupling strengths
where the spectral statistics is of Wigner-Dyson type, while wave functions are
non-uniformly distributed over Fock space and show fractal behavior. The
structure of the theory suggests that such manifestations of non-ergodic
extendedness may be a prevalent phenomenon in strongly interacting chaotic
quantum systems.
