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arXiv:1711.06310 · Physical review. B./Physical review. B

Local density of the Bose-glass phase

Kalani Hettiarachchilage, Conrad Moore, V. G. Rousseau, Ka-Ming Tam, Mark Jarrell, Juana Moreno

Published Nov 26, 2018• 6 citations
arXivHTMLPDF

Abstract

We study the local density of the Bose-Hubbard model in the presence of on-site disorder near the Bose-glass transition using multifractal, typical medium, and percolation theories. At incommensurate filling our findings support the scenario of percolating superfluid clusters enhancing Anderson localization. Scaling analysis of the superfluid density at the incommensurate filling of $\ensuremath{\rho}=1.1$ and on-site interaction $U=80t$ predicts a superfluid-Bose-glass transition at disorder strength of ${\mathrm{\ensuremath{\Delta}}}_{c}\ensuremath{\approx}30t$. At this filling the local-density distribution becomes more skew with increasing disorder strength. Multifractal analysis suggests a multifractal behavior resembling that of the Anderson localization. In the Bose-glass phase the mode of the local-density distribution approaches an integer value as expected from typical medium theory for the Anderson localization. Percolation analysis points to a phase transition of percolating noninteger filled sites around the same value of disorder. On the other hand, the behavior at commensurate filling is rather different. Close to the tip of the Mott lobe ($\ensuremath{\rho}=1,U=22t$) we find a Mott-insulator-Bose-glass transition at disorder strength of ${\mathrm{\ensuremath{\Delta}}}_{c}\ensuremath{\approx}16t$. An analysis of the local-density distribution shows Gaussian-like behavior for a wide range of disorders above and below the transition.

DOI
10.1103/physrevb.98.184206

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We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization-group analysis of the corresponding effective-field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping-disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica-mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable toward the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.
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We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify an order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of $\ensuremath{\nu}=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $\ensuremath{\gamma}=4/D\ensuremath{-}1$ at the transition. At commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant.
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