Influence of counter-rotating interaction on quantum phase transition in   Dicke-Hubbard lattice: an extended coherent state approach
  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. 
Yongchuan Lu and Chen Wang
quant-ph