Symmetry-protected coherent relaxation of open quantum systems

We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin- 1/2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between PT symmetry and weak symmetries, which strengthens previous predictions for PT-symmetric Liouvillian dynamics. Requirements are a nondegenerate PT-symmetric generator of time evolution ^L, a weak parity symmetry, and an observable that is antisymmetric under this parity transformation. The spectrum of ^L then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.