Recent experimental and numerical studies of the critical-temperature exponent φ for the superfluid-Bose glass universality in three-dimensional systems report strong violations of the key quantum critical relation, φ = νz, where z and ν are the dynamic and correlation length exponents, respectively, and question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), Tc ∝ (µ − µc) φ , was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the φ = νz law [with φ = 2.7(2), z = 3, and ν = 0.88(5)] holds true, resolving the φ-exponent "crisis".PACS numbers: 67.85. Hj,64.70.Tg Disordered Bose-Hubbard (DBH) model is frequently employed as a key prototype system to discuss and understand a number of important experimental cases, such as 4 He in porous media and on various substrates, thin superconducting films, cold atoms in disordered optical lattice potentials, and disordered magnets (see [1,2] and references therein), etc.The pioneering work [3,4] on the DBH model has established that at T = 0 an insulating Bose glass (BG) phase will emerge as a result of localization effects in disordered potentials. On a lattice, this phase will intervene between the Mott-insulator (MI) and superfluid (SF) phases at arbitrary weak disorder strength [4,5] and completely destroy the MI phase at strong disorder. In contrast with the gapped incompressible MI phase, the BG phase has finite compressibility, κ, due to finite density of localized gapless quasiparticle and quasihole excitations. Using scaling arguments, and the fact that κ = const at the critical point of the quantum SF-BG transition, it was predicted that the dynamic critical exponent, z, always equals the dimension of space; i.e., z = d [4]. The decrease of the normal-to-superfluid transition temperature, T c , on approach to the quantum critical point (QCP) is characterized by the φ exponent:where g is the control parameter used to reach the QCP. Standard scaling analysis of the quantum-critical free-energy density predicts that φ has to satisfy the relation φ = νz. Therefore, taking into account Harris criterion ν ≥ 2/d [6] for the correlation length exponent in disordered systems, it is expected that φ ≥ 2, within the standard picture of quantum critical phenomena.Despite substantial research efforts in the last two decades, some aspects of the universal critical behavior described above remain controversial (see, e.g., Ref. [7]).For instance, Ref. [8] argues that finite κ at the SF-BG critical point might come from the regular analytic (rather than singular critical) part of the free energy, and, thus, z < d should be considered as an undet...

We present an asymptotically exact renormalization-group theory of the superfluid-insulator transition in one-dimensional (1D) disordered systems, with emphasis on an accurate description of the interplay between the Giamarchi-Schulz (instanton-anti-instanton) and weak-link (scratched-XY) criticalities. Combining the theory with extensive quantum Monte Carlo simulations allows us to shed new light on the ground-state phase diagram of the 1D disordered Bose-Hubbard model at unit filling. c KF , a single arbitrarily weak impurity gets renormalized to an infinitely high (in relative low-energy units) barrier; for > K K c KF , by contrast, the link gets progressively healed with increasing length scale and becomes asymptotically transparent.A controlled theory of SF-BG transition in 1D, yielding, in particular, = K 3 2 c , was first developed by Giamarchi and Schulz (GS) using a perturbative RG treatment of disorder [6]. In the same work, the authors conjectured that there might exist an alternative strong-disorder scenario not captured by their theory. Subsequently, some of us demonstrated [3] that the GS result is valid beyond the lowest-order RG equations and is, in fact, a generic answer thanks to the above-mentioned asymptotically exact mechanism of instanton-antiinstanton proliferation, which is tantamount to the arguments presented in the original papers by Kosterlitz and Thouless. A 'strong-disorder' alternative therefore seems unlikely. Nevertheless, Altman et al, inspired by the 1D-specific classical-field mechanism of destroying global SF stiffness by anomalously rare but anomalously weak links, speculated that an alternative strong-disorder scenario does exist [8]. To corroborate their idea, the authors employed a real-space RG treatment. It is important to realize, however, that the treatment of [8] is essentially uncontrolled, abandoning the usual LL paradigm in favor of the 'Coulomb blockade' single-particle nomenclature promoted to macroscopic scales.This, in turn, was countered by the theorem of critical self-averaging, which implies that the LL picture holds at criticality [9]. In combination with the Kane-Fisher result that a single weak link is an irrelevant perturbation at > K 1, this seemed to leave no room for alternatives to the GS scenario because no other asymptotically exact mechanisms for destruction of superfluidity were known. However, recently three of us have realized [10] that previous studies have overlooked the difference in the outcome of the Kane-Fisher renormalization for weak links, which occur with finite probability per unit length, relative to the one for a single link in an infinite system. The difference is in the classical-field mechanism of suppressing the SF stiffness by weak links (for a discussion, see [9,11]): in absolute units, the Kane-Fisher renormalization is always towards making links weaker-and the weaker the link, the stronger its effect on Λ. Despite the fact that at > K 1 a single weak link cannot destroy superfluidity, the combined effect of all anomalously...

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1168 (2019)] has realized a dynamical gauge system with a Z 2 gauge symmetry in a double-well potential. In this work we propose a method to generalize this model from a single double well to a one-dimensional chain. We show that although there are no disordered potentials in the original model, the phenomenon of many-body localization can occur. The key ingredient is that different symmetry sectors with different local gauge charges play the role of different disorder configurations, which becomes clear after exactly mapping our model to a transverse Ising model in a random longitudinal field. We show that both the ergodic regime and the many-body localized regime exist in this model from four different metrics, which include level statistics, volume law versus area law of entanglement entropy of eigenstates, quench dynamics of entanglement entropy, and physical observables.