Classical-Field Renormalization Flow of One-Dimensional Disordered Bosons

Abstract

We show that in the regime when strong disorder is more relevant than field quantization the superfluid--to--Bose-glass criticality of one-dimensional bosons is preceded by the prolonged logarithmically slow classical-field renormalization flow of the superfluid stiffness at mesoscopic scales. With the system compressibility remaining constant, the quantum nature of the system manifests itself only in the renormalization of dilute weak links. On the insulating side, the flow ultimately reaches a value of the Luttinger parameter at which the instanton--anti-instanton pairs start to proliferate, in accordance with the universal quantum scenario. This happens first at astronomic system sizes because of the suppressed instanton fugacity. We illustrate our result by first-principles simulations.

11 pages, 14 figures + references

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Cited by in corpus (19)

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• Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension
• A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder
• Asymptotically Exact Scenario of Strong-Disorder Criticality in One-Dimensional Superfluids
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Superfluid/Bose-glass transition in one dimension
• Numerical evidence for strong randomness scaling at a superfluid-insulator transition of one-dimensional bosons
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• Superfluid--Insulator Transition in Strongly Disordered One-dimensional Systems
• Localization of disordered bosons and magnets in random fields
• Superfluid-insulator transition of two-dimensional disordered Bose gases
• Susceptibility at the Superfluid-Insulator Transition for One-Dimensional Disordered Bosons
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• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the Sine-Gordon transition: a Worm Algorithm Monte Carlo study
• Strong randomness criticality in the scratched-XY model