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 $K$. In contrast to the scenario by Altman {\it et al.} [Phys. Rev. B {\bf 81}, 174528 (2010)], the hydrodynamic description is valid under the correlation radius and defines criticality via the renormalization of microscopically weak links, along the lines of Kane and Fisher [Phys. Rev. Lett. {\bf 68}, 1220 (1992)]. The hallmark of the theory is the relation $K^{(c)}=1\mathrm{/}\zeta$ between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent $\zeta$ describing the scaling $\propto 1\mathrm{/}{N}^{1-\zeta }$ for the strength of the weakest link among the $N\mathrm{/}L\gg 1$ disorder realizations in a system of fixed mesoscopic size $L$.