Nonergodic Extended States in the Sachdev-Ye-Kitaev Model

We analytically study spectral correlations and many body wave functions of a Sachdev-Ye-Kitaev model deformed by a random Hamiltonian diagonal in Fock space. 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 nonuniformly distributed over Fock space. The structure of the theory suggests that such manifestations of nonergodic extendedness may be a prevalent phenomenon in many body chaotic quantum systems.