We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.PACS numbers: 64.60. Cn, 03.75.Hh, 05.30.Jp, An interplay between commensurability, interactions, and disorder in the superfluid-insulator quantum phase transition is a challenging theoretical problem with applications to such diverse physical systems as 4 He in porous media and aerogels, superfluid films on various substrates, Josephson junction arrays, granular superconductors, disordered magnets, etc. (see, e.g., [1,2,3,4,5,6], and references therein). Recently, research on disordered bosons is strongly stimulated by the possibility of controlled experiments with ultracold atomic systems [7,8].Commensurability is relevant for the system of lattice bosons with the off-diagonal disorder (random hopping amplitude or on-site repulsion) and exact particlehole symmetry (taking place in the limit of large filling factor) [9]. It leads to a new type of insulator, incompressible and gapless Mott glass (MG) [10] in place of incompressible gapped Mott insulator (MI). In twodimensional (2D) systems, changing the nature of the insulating phase results in the new universality class of the superfluid-insulator (SF-I) transition. The SF-MG transition is characterized by the dynamical critical exponent 1 < z < 2 different from z = 1 for the SF-MI point in a perfect system [5]. A similar situation is expected in 3D.Surprisingly, very little is known for fact about the 1D case apart from perturbative renormalization group (RG) arguments. On the superfluid side of the transition, one can use the instanton language [11] in terms of which weak off-diagonal disorder does not seem to be relevant, leading only to the inhomogeneity of the microscopic stiffness in the equivalent (1+1)D classical XY model. Recently, Altman et al.[6] argued on the basis of the spatial RG analysis that while small off-diagonal disorder is indeed irrelevant for the SF-MG criticality, there should exist also the strong-randomness fixed point. We are not aware of any large-scale numerical simulations attempting to study the SF-MG criticality in the strongly disordered system.The main observable of interest in 1D systems is the Luttinger-liquid parameter g = π √ Λκ, where Λ is the superfluid stiffness and κ is the compressibility. There is a "smoking gun" signature in the behavior of g at the critical point which allows to discriminate between different scenarios of the phase transition. If the SF-MG transi...

In recent experiments on thin 4 He films absorbed to rough surfaces Luhman and Hallock (Ref. 1) attempted to observe KT features of the superfluid-normal transition of this strongly disordered 2D bosonic system. It came as a surprise that while peak of dissipation was measured for a wide range of surface roughness there were no indications of the theoretically expected universal jump of the areal superfluid density for the strongly disordered samples. We test the hypothesis that this unusual behavior is a manifestation of finite-size effects by numerical study of the corresponding 2D bosonic model with strong diagonal disorder. We demonstrate that the discontinuous features of the underlying KT transition are severely smoothed out for finite system sizes (or finite frequency measurements). We resolve the universal discontinuity of the areal superfluid density by fitting our data to the KT renormalization group equations for finite systems. In analogy to our simulations, we suggest that in experiments on strongly disordered 2D bosonic systems the very existence of the KT scenario can and should be revealed only from a proper finite-size scaling of the data (for 4 He films finite-size scaling can be effectively controlled by the scaling of finite frequency of measurements). We also show relevance of our conclusions for a wider class of systems, such as superconducting granular films, Josephson junction arrays, and ultracold atomic gases, where similar difficulties appear in experiments designed to verify KT transition (especially in disordered cases).