  We investigate the ground state behavior of the Dicke-Hubbard model including
counter-rotating-terms. By generalizing an extended coherent state approach
within mean-field theory, we self-consistently obtain the ground state energy
and delocalized order parameter. Localization-delocalization quantum phase
transition of photons is clearly observed by breaking the parity symmetry.
Particularly, Mott lobes are fully suppressed, and the delocalized order
parameter shows monotonic enhancement by increasing qubit-cavity coupling
strength, in sharp contrast to the Dicke-Hubbard model under rotating-wave
approximation. Moreover, the corresponding phase boundaries are stabilized by
decreasing photon hopping strength, compared to the Rabi-Hubbard model.
