Exploring quantum phases by driven dissipation

Ever since the insight spreaded that tailored dissipation can be employed to control quantum systems and drive them towards pure states, the field of non-equilibrium quantum mechanics gained remarkable momentum. So far research focussed on emergent phenomena caused by the interplay and competition of unitary Hamiltonian and dissipative Markovian dynamics. In this manuscript we zero in on a so far rather understudied aspect of open quantum systems and non-equilibrium physics, namely the utilization of purely dissipative couplings to explore pure quantum phases and non-equilibrium phase transitions. To illustrate this concept, we introduce and scrutinize purely dissipative counterparts of (1) the paradigmatic transverse field Ising model and (2) the considerably more complex $\mathbb{Z}_2$ lattice gauge theory with coupled matter field. We show that, in mean field approximation, the non-equilibrium phase diagrams parallel the (thermal) phase diagrams of the Hamiltonian "blue print" theories qualitatively.