Algebraic localization from power-law couplings in disordered quantum wires

We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance x as a power law 1/x^a. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long- distance algebraic decay of correlations within disordered-localized phases, for all exponents a. The exponent of algebraic decay depends only on a, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular, and solid-state physics.