Superfluid-Insulator Transition in a Commensurate One-Dimensional Bosonic System with Off-Diagonal Disorder

Abstract

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...

Superfluid/Bose-glass transition in one dimension

“…What happens for larger disorder or weaker interactions is still an open question. [23][24][25][26][27] One possibility is of course that the exponent remains universal along the whole line. In that case, there is most likely a unique Bose glass phase.…”

“…(42) can be evaluated in a series expansion in the small parameter δ that is defined in Eq. (23). The details of calculation are presented in Appendices A,B, and C, while here we state the final results.…”

A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

“…An older study [80] in 1d found a Kosterlitz-Thouless transition compatible with a universal Luttinger value (cf. [1,2]), but the disorder was too weak to see the physics mentioned in Ref.…”

Quantum Glass Phases in the Disordered Bose-Hubbard Model

“…hopping or interaction strengths, have remained largely unexplored until recently, when it was demonstrated that these can lead to qualitatively quite different phenomena [19,20,21]. In the quantum rotor model with off-diagonal disorder, the SF to MI transition takes place via an intermediate Mott glass (MG) phase [20,21]-a unique incompressible, yet gapless, glassy regime that was first reported in disordered fermions with extended range interactions [22]. It is thus of great interest to investigate whether such a phase also appears in the Bose-Hubbard model (BHM), and if particle-hole symmetry is essential for the stabilization of such a MG.…”