Symmetric dynamics in dissipative quantum many-body models

We show symmetric dynamics in dissipative quantum many-body systems. Given some conditions on the Hamiltonian and the jump operators, the time evolution of certain observables can be identical for ferromagnetic and antiferromagnetic interactions in an Ising model with external fields or for repulsive and attractive interactions in a Hubbard model. We present two theorems to determine the existence of such a dynamical symmetry in dissipative quantum systems. The symmetry under the steady state is present independently on the initial state. Further constraint on the initial state leads to a stronger dynamical symmetry in real-time evolutions. We demonstrate the application of our theorems in dissipative Ising and Hubbard models. In addition, for the Fermi-Hubbard model, our results also reveal a connection between spin and charge densities in dissipative dynamics. We validate the discussions with numerical simulations performed using tensor network algorithms.