Universality in driven open quantum matter

Universality is a powerful concept that enables qualitative and quantitative predictions to be made in systems with extensively many degrees of freedom. It finds realizations in almost all branches of physics, including in the realm of nonequilibrium systems. The focus of this review is on universality's manifestations within a specific class of nonequilibrium stationary states: driven open quantum matter. Progress in this field is fueled by a number of increasingly prominent platforms ranging from light-driven quantum materials over synthetic quantum systems like cold atomic gases to the functional devices of the noisy intermediate-scale quantum era. These systems share the characteristic that, on the microscopic scale, they obey the laws of quantum mechanics, while detailed balance underlying thermodynamic equilibrium is broken owing to the simultaneous presence of Hamiltonian unitary dynamics and nonunitary drive and dissipation. The challenge is then to connect this microscopic physics to macroscopic observables and to identify universal collective phenomena that uniquely witness the breaking of equilibrium conditions, thus having no equilibrium counterparts. In the framework of a Lindblad-Keldysh field theory, on the one hand, this review discusses the principles delimiting thermodynamic equilibrium from driven open stationary states, and, on the other hand, it is shown how unifying concepts such as symmetries, the purity of states, and scaling arguments are implemented. Then presented are instances of universal behavior structured into three classes: new realizations of paradigmatic nonequilibrium phenomena, including a survey of first experimental realizations; novel instances of nonequilibrium universality found in these systems made of quantum ingredients; and genuinely quantum phenomena out of equilibrium, including in fermionic systems. Perspectives for future research on driven open quantum matter are also discussed.