Symmetric dynamics in dissipative quantum many-body models

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