Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

Abstract

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...

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