Algebraic localization of disordered long-range quantum models
Several atomic, molecular, and optical systems, as well as certain condensed matter models, exhibit long-range interactions that decay with distance r as a power law 1/r^alpha. In this talk, we will present recent results for the localization properties of correlation functions of these long-range quantum models in the presence of disorder. The latter is usually associated with exponential localization of wave functions and correlations. We demonstrate that in most situations in 1D power-law interactions imply algebraic decay of correlations. We will discuss the generality of these results and their application to experiments in atomic and molecular physics.