  Recently, the authors of the commented PRL presented the $ N=\infty $
solution of the $ U(1)/Z_2 $ Dicke model studied by us previously.
  Here we point out that
  (1) The authors missed an important transformation relating the two parameter
regimes, so their separate discussions on the two regimes is redundant.
  (2) Both $ N=\infty $ classical limit and $ 1/N $ quantum fluctuations have
been achieved in two of our previously published papers. It is the $ 1/N $
quantum fluctuations which lead to the non-trivial new quantum phenomena. In
view of only a few $ N=2\sim 9 $ qubits inside a circuit QED microwave cavity,
they can be tested in near future experiments.
  (3) Several possible experimental implementations of the $ U(1)/Z_2 $ Dicke
model have been proposed before and recently experimentally realized.
