Not yet reviewed by Pith; the record is open.

We study the ergodic and non-ergodic behaviors of a clean Jaynes-Cummings-Hubbard chain for different parameters based on the average level spacings and the generalized fractal dimensions of eigenstates by using exact diagonalization. It can be found that a transition from ergodicity to non-ergodicity phases happens when the atom-photon detuning is large, and the non-ergodic phases maybe exist in the thermodynamic limit. We also find that the non-ergodic phase violates the eigenstate thermalization hypothesis. Finally, we study the many-body multifractality of the ground state and find that the derivative of the generalized fractal dimensions can determine the critical point of the Superfluid-Mott-insulation phase transition in a small range of parameters under different boundary conditions and there is no ergodicity for the ground state.