  We consider a generalized Dicke model with U(1) symmetry, which can undergo a
transition to a superradiant state that spontaneously breaks this symmetry. By
exploiting the difference in timescale between atomic and cavity dynamics, one
may eliminate the cavity dynamics, providing an atom-only theory. We show that
the standard Redfield theory cannot describe the transition to the superradiant
state, but including higher-order corrections does recover the transition. Our
work reveals how the forms of effective theories must vary for models with
continuous symmetry, and provides a template to develop effective theories of
more complex models.
