Asymptotically exact scenario of strong-disorder criticality in one-dimensional superfluids

We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the Luttinger parameter K. The hydrodynamic description is valid under the correlation radius and defines criticality via mutual renormalization of the strength of microscopic weak links and superfluid stiffness. The link strength renormalizes along the lines of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)], while the renormalization of superfluid stiffness follows the lines of classical-field flow. The hallmark of the theory is the relation K-(c) = 1/zeta between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent zeta describing the scaling proportional to 1/N1-zeta for the strength of the weakest link among the N >> L disorder realizations in a system of fixed mesoscopic size L.