  We investigate the decoherence dynamics of continuous variable entanglement
as the system-environment coupling strength varies from the weak-coupling to
the strong-coupling regimes. Due to the existence of localized modes in the
strong-coupling regime, the system cannot approach equilibrium with its
environment, which induces a nonequilibrium quantum phase transition. We
analytically solve the entanglement decoherence dynamics for an arbitrary
spectral density. The nonequilibrium quantum phase transition is demonstrated
as the system-environment coupling strength varies for all the Ohmic-type
spectral densities. The 3-D entanglement quantum phase diagram is obtained.
