  We show that the dynamical symmetry exists in dissipative quantum many-body
systems. Under constraints on both Hamiltonian and dissipation parts, the time
evolution of particular observables can be symmetric between repulsive and
attractive interactions in the Hubbard model, or symmetric between
ferromagnetic and anti-ferromagnetic interactions in the Ising model with
external fields. We present a theorem to determine the existence of the
dynamical symmetry in dissipative systems. This theorem is also responsible for
the symmetry of steady states, even without the constraint on the initial
state. We demonstrate the applications of our theorem with numerical
simulations using tensor network algorithms.
