Fate of symmetry protected coherence in open quantum system

We investigate the fate of coherence in the dynamical evolution of symmetry protected quantum systems. Under the formalism of system plus bath for open quantum systems, antiunitary symmetries exhibit significant differences from the unitary ones in protecting initial coherence. Specifically, taking advantage of the Lindblad master equation, we find that a pure state in the symmetry protected degenerate subspace will be decoherent even though both the system Hamiltonian and system-environment interaction respect the same antiunitary symmetry. In contrast, the coherence will persist when the protecting symmetry is unitary. We provide an elaborate classification table to illustrate what kinds of symmetry combinations are able to preserve the coherence of the initial state, which is confirmed in several concrete models of single spin-3/2 systems. It can also be applied to the Haldane phase in interacting topological systems. Our results could be helpful in exploring possible experimental realization of stable time-reversal symmetric topological states.