Noise-driven quantum criticality

We discuss a notion of quantum critical exponents in open quantum many-body systems driven by quantum noise. We show that in translationally invariant quantum lattice models undergoing quasi-local Markovian dissipative processes, mixed states emerge as stationary points that show scaling laws for the divergence of correlation lengths giving rise to well-defined critical exponents. The main new technical tool developed here is a complete description of steady states of free bosonic or fermionic translationally invariant systems driven by quantum noise: This approach allows to express all correlation properties in terms of a symbol, paralleling the Fisher-Hartwig theory used for ground state properties of free models. We discuss critical exponents arising in bosonic and fermionic models. Finally, we relate the findings to recent work on dissipative preparation of pure dark and matrix product states by Markovian noisy processes and sketch further perspectives.