Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas

We determine the phase diagram of a one-dimensional Bose gas in the presence of disorder with short- and long-range correlations, the latter decaying with distance as 1/|x|^1+. When c=3-²/3 -0. 289868, and a Mott glass -- characterized by a vanishing compressibility and a gapless conductivity -- when <c. Our conclusions, based on the nonperturbative functional renormalization group and perturbative renormalization group, are confirmed by the study of the case =-1, corresponding to a perfectly correlated disorder in space, where the model is exactly solvable in the semiclassical limit K 0^+.