Defining Stable Phases of Open Quantum Systems
At school, we’re taught that there are three phases of matter: liquid, solid, and gas. But this is wrong, as many more phases are possible at low temperatures, where quantum mechanics can lead to a host of exotic effects like superconductivity. The theoretical search for new phases has tended to assume that they are in thermal equilibrium with their environments. What sorts of phases might be possible if we remove that assumption? What confers on these “open phases” the robustness associated with bona fide phases of matter?
Our work identifies a property shared by many open phases that accounts for their stability and narrows the search for new examples. Modern quantum simulators allow us to entangle degrees of freedom in the underlying quantum bits and perform measurements, the results of which might affect what we do next. In following such a recipe, an experimentalist implements a quantum channel. Repeated applications of a channel drive a system toward a steady state—essentially, a phase of matter.
Our work sets out a sufficient condition for the correlations of those steady states to be stable to perturbations and noise. Roughly, this condition (called uniformity) says that the steady states of perturbed channels, which are akin to open phases, relax quickly to those of the unperturbed channel under the unperturbed dynamics.
Authors: Tibor Rakovszky, Sarang Gopalakrishnan, Curt von Keyserlingk