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Dynamical symmetry in quantum dissipative models

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.