  We study both mean-field and full quantum dynamics of symmetry-breaking
transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By
controlling s-wave scattering lengths and coupling strength, it is possible to
stimulate SBTs between normal and spontaneously polarized ground states. In
static transitions, the probability maxima of full quantum ground states
correspond to the mean-field ground states. In dynamical transitions, due to
the vanishing of excitation gaps, the mean-field dynamics shows universal
scalings obeying Kibble-Zurek mechanism. Both mean-field and full quantum
defect modes appear as damped oscillations, but they appear at different
critical points and undergo different oscillation regimes. The anomalous
breakdown of mean-field dynamics induced by SBTs depends on the approaching
direction.
