Variational principle for steady states of dissipative quantum many-body systems.

We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the dynamics. We show how to apply this approach to different classes of variational quantum states and demonstrate its successful application to a dissipative extension of the Ising model, which is of importance to ongoing experiments on ultracold Rydberg atoms, as well as to a driven-dissipative variant of the Bose-Hubbard model. Finally, we identify several advantages of the variational approach over previously employed mean-field-like methods.