Superfluid clusters, percolation and phase transitions in the disordered, two-dimensional Bose–Hubbard model

Niederle, Astrid Elisa; Rieger, Heiko

doi:10.1088/1367-2630/15/7/075029

Cited by 52 publications

(99 citation statements)

References 47 publications

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“…A similar comparison between QMC and Gutzwiller data has been reported in Ref. [38] for a 2D lattice. There, the percolation of sites with noninteger occupation (defined to within a certain accuracy) was studied.…”

Section: S 'supporting

confidence: 84%

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Interacting bosons in a disordered lattice: Dynamical characterization of the quantum phase diagram

Buonsante¹,

Pezzé

Smerzi

2015

Phys. Rev. A

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We study the quantum dynamics of interacting bosons in a three-dimensional disordered lattice. We show that the superfluid current induced by an adiabatic acceleration of the disordered lattice undergoes a dynamical instability signaling the onset of the Bose-glass phase. The dynamical superfluid-Bose-glass phase diagram is found in very good agreement with static superfluid fraction calculation. A different boundary is obtained when the disorder is suddenly quenched in a moving periodic lattice. In this case we do not observe a dynamical instability but rather a depletion of the superfluid density. Our analysis is based on a dynamical Gutzwiller approach which we show to reproduce the quantum Monte Carlo static phase diagram in the strong interaction limit.How does disorder affect superfluidity? This question [1,2], first posed for liquid helium [3] in the 1980s, remains-to a large extent and in spite of a large body of results-an open and challenging problem. The literature has mainly focused on the ground-state properties of zero-temperature interacting bosons in a disordered potential (the "dirty boson" problem [4]), which is either superfluid (SF) or insulating. The insulating phases can be of two different kinds. If disorder dominates over interaction, the system is found in a gapless Bose-glass (BG) phase consisting of disconnected SF puddles. If interaction is sufficiently strong and dominates over disorder, a lattice system at integer filling is a Mott insulator (MI), characterized by a gap in the excitation spectrum that prevents the exchange of particles between neighboring sites. However, while "static" properties of dirty bosons are well understood, much less is known about the effect of disorder on the dynamical SF properties [5].Experiments with ultracold gases have renewed the interest in disorder [6] and lattice [7] physics. In these systems, the SF-MI transition has been observed in spectacular experiments [8], Anderson localization has been demonstrated in one [9] and three (3D) [10,11] dimensions, and the SF-BG transition is currently under intense investigation [12][13][14][15]. Ultracold gases offer the fine control of relevant parameters and unprecedented diagnostics: spatial and momentum distributions can be directly imaged and, as demonstrated in recent experiments [15][16][17][18], dynamical excitations can be probed.In this Rapid Communication we analyze the dissipation mechanism of the SF current in a system of dilute interact ing bosons at zero temperature in a 3D disordered lattice. The quantum dynamics is investigated in the Gutzwiller approximation. We prepare the system in the ground state of the disordered lattice, which we subsequently accelerate adiabatically up to a final velocity (we refer to this as boost protocol). The current induced by this boost either persists substantially unchanged for the entire-comparatively long-observation time, or rapidly decays due to dynamical instabilities [19]. We recognize two different regions in the disorder versus interaction plane, which...

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Section: S 'supporting

confidence: 84%

“…The percolation threshold found in Ref. [38] well reproduces the SF critical line determined by QMC simulations in Ref. [39].…”

Section: S 'supporting

confidence: 77%

Interacting bosons in a disordered lattice: Dynamical characterization of the quantum phase diagram

Buonsante¹,

Pezzé

Smerzi

2015

Phys. Rev. A

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“…The results obtained for the superfluid border using a proper superfluid fraction reproduce, in fact, the percolation border of [56] with quite a good accuracy. They are shown below together with the HF percolation threshold.…”

Section: Gutzwiller-ansatzmentioning

confidence: 56%

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

et al. 2014

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We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the sitedependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points however, cease to exists after the addition of the hopping disorder.

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“…It is in the difficult intermediate parameter space where the BG phase obtains. It has been argued by various authors 1,[3][4][5][6][7] that the BG is a quantum Griffiths phase dominated by arbitrarily large SF regions that are, however, exponentially suppressed. Despite the abundance of numerical 3,[8][9][10][11][12][13] and analytical [14][15][16][17][18][19][20][21][22][23] work on the subject, it is only recently that several aspects of this model have been fully understood.…”

Section: Introductionmentioning

confidence: 99%

“…4. Other omputational methods have produced a phase boundary on the same order of magnitude with the same characteristic shape 7 . At the transition to the MI, the correlation length diverges as a power law, ξ ∼ (t − t c ) −ν .…”

mentioning

confidence: 99%

Breakdown of self-averaging in the Bose glass

2013

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We study the square-lattice Bose-Hubbard model with bounded random on-site energies at zero temperature. Starting from a dual representation obtained from a strong-coupling expansion around the atomic limit, we employ a real-space block decimation scheme. This approach is non-perturbative in the disorder and enables us to study the renormalization-group flow of the induced random-mass distribution. In both insulating phases, the Mott insulator and the Bose glass, the average mass diverges, signaling short range superfluid correlations. The relative variance of the mass distribution distinguishes the two phases, renormalizing to zero in the Mott insulator and diverging in the Bose glass. Negative mass values in the tail of the distribution indicate the presence of rare superfluid regions in the Bose glass. The breakdown of self-averaging is evidenced by the divergent relative variance and increasingly non-Gaussian distributions. We determine an explicit phase boundary between the Mott insulator and Bose glass.

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Superfluid clusters, percolation and phase transitions in the disordered, two-dimensional Bose–Hubbard model

Cited by 52 publications

References 47 publications

Interacting bosons in a disordered lattice: Dynamical characterization of the quantum phase diagram

Interacting bosons in a disordered lattice: Dynamical characterization of the quantum phase diagram

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

Breakdown of self-averaging in the Bose glass

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