Application of a multisite mean-field theory to the disordered Bose-Hubbard model

Pisarski, P.; Jones, R. M.; Gooding, R. J.

doi:10.1103/physreva.83.053608

Cited by 36 publications

(50 citation statements)

References 34 publications

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“…Apart from the considerable work done on the disordered BH model [1,4,5,12,13], the model has also been extended to superlattices [7,[14][15][16][17][18][19][20][21][22], spinor condensates [23][24][25], multicomponent systems [22,[26][27][28], and multiband situations [29][30][31]. With increasing complexity, the MI-SF phase diagram becomes increasingly richer in structure.…”

Section: Introductionmentioning

confidence: 99%

Multisite mean-field theory for cold bosonic atoms in optical lattices

et al. 2012

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We present a detailed derivation of a multisite mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean-field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a nontrivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to d-dimensional hypercubic lattices in one, two, and three dimensions and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for d = 3. The MSMFT is then used to examine a linear dimer chain in which the onsite energies within the dimer have an energy separation of . This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.MCINTOSH, PISARSKI, GOODING, AND ZAREMBA PHYSICAL REVIEW A 86, 013623 (2012) II. FORMALISM: MULTISITE MEAN-FIELD THEORY A. Derivation in one dimensionOur work is based on the BH Hamiltonian [2] in the grand canonical ensemble. With the assumption of a single orbital per site, this Hamiltonian is given bywhere the index i labels the sites of the optical lattice andĉ † i andĉ i are site creation and annihilation operators (henceforth referred to as site operators), respectively; the number operator for site i is given byn i =ĉ † iĉ i . The system parameters include the onsite energies ε i at each lattice site, the tunneling energy J ij between sites i and j , and the intrasite interaction energy U i . To a good approximation it is sufficient to ignore interactions between bosons on different sites and hopping between sites further apart than the nearest-neighbor distance [2,37]. Furthermore, we will restrict our considerations to the case where the interaction parameter has a common value U for all sites and a hopping parameter J for all nearest-neighbor pairs. Generalizations to more complex situations such as superlattices [15][16][17] can be readily accommodated in the MSMFT that we develop. The final parameter in the BH Hamiltonian is the chemical potential μ which controls the 013623-2 013623-3 MCINTOSH, PISARSKI, GOODING, AND ZAREMBA PHYSICAL REVIEW A 86, 013623 (2012)

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Section: Introductionmentioning

confidence: 99%

Multisite mean-field theory for cold bosonic atoms in optical lattices

et al. 2012

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“…Moreover the authors suggest that the presence of the BG surrounding the MI phase could be inferred from the spectral properties of the random matrix, which appear in the linearized problem. In [55] the authors generalize the inhomogeneous site-dependent mean-field to clusters, which allows them to include the (short-range) spatial correlations. Sheshadri and co-workers [53] proposed to study the Bose-Hubbard model with disordered potential using the inhomogeneous generalization of the site-decoupling mean-field method, i.e., the local meanfield theory .…”

Section: Brief Survey Of Mean-field Approaches For the Disorderedmentioning

confidence: 99%

“…Our main results are: i) for the Hamiltonian H 1 there is a direct MI-SF transition at the tips of the Mott lobes in the thermodynamic limit; ii) for the Hamiltonian H 2 the Mott lobes are smaller, and the direct MI-SF transition at their tips disappears, although the region of BG is very narrow; iii) finally, for H 3 there is no direct MI-SF transition and the region of BG is wider in comparison to H 2 . One of the main aspects of this paper is also the use of the mean-field theory combined with the simple Hartree-Fock approach, quite different from what has been proposed so far [52][53][54][55][56][57][58], and quite efficient in determining the phase boundary between the BG and the SF phase.…”

Section: Introductionmentioning

confidence: 99%

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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“…Although the Gutzwiller method has common restrictions of the mean-field methods, it has provided versatile applications in qualitative calculations of both stationary states and time-evolution dynamics. In recent, cluster bosonic Gutzwiller methods [29][30][31][32][33][34] have been developed by coupling multi-site clusters rather than single sites with the mean field. By employing the cluster Gutzwiller method, some properties of many-body LZ phenomena in repulsive BHL [35] and some quantum phases in attractive BHL [36] have been explored.…”

Section: Introductionmentioning

confidence: 99%

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

et al. 2015

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We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For a unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the inter-chain tunneling is much stronger than the intra-chain one. The fractional insulator phases can not be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the inter-chain bias. In the many-body Landau-Zener process, in which the inter-chain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

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Application of a multisite mean-field theory to the disordered Bose-Hubbard model

Cited by 36 publications

References 34 publications

Multisite mean-field theory for cold bosonic atoms in optical lattices

Multisite mean-field theory for cold bosonic atoms in optical lattices

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

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

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