Ergodic and nonergodic phases in a one-dimensional clean Jaynes-Cummings-Hubbard system with detuning

We study the ergodic and nonergodic behaviors of a clean Jaynes-Cummings-Hubbard chain for different parameters based on the average level spacing ratios and the generalized fractal dimensions of eigenstates by using exact diagonalization. It can be found that a transition from ergodic to nonergodic regimes happens when increasing the atom-photon detuning, and the nonergodic phases should exist in the thermodynamic limit. We also find that the nonergodic phase violates the eigenstate thermalization hypothesis and displays many-body-localization-like behavior. 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.