Phase transitions in an interacting boson model with near-neighbor repulsion

Niyaz, Parhat; Scalettar, Richard; Fong, C. Y.; Batrouni, G. G.

doi:10.1103/physrevb.50.362

Cited by 49 publications

(41 citation statements)

References 29 publications

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“…Therefore the model has been intensively studied both analytically [1,3,4,5] as well as numerically [6,7,8,9,10,11,12,13] in recent years. In the absence of a trapping potential, i.e., for the homogeneous Bose-Hubbard model, a quantum phase transition from a superfluid to a Mott-insulating phase occurs at commensurate fillings upon increasing the optical lattice depth [3].…”

Section: Introductionmentioning

confidence: 99%

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

et al. 2006

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We report results of quantum Monte Carlo simulations in the canonical and the grand-canonical ensemble of the two-and three-dimensional Bose-Hubbard model with quadratic and quartic confining potentials. The quantum criticality of the superfluid-Mott insulator transition is investigated both on the boundary layer separating the two coexisting phases and at the center of the traps where the Mott-insulating phase is first established. Recent simulations of systems in quadratic traps have shown that the transition is not in the critical regime due to the finite gradient of the confining potential and that critical fluctuations are suppressed. In addition, it has been shown that quantum critical behavior is recovered in flat confining potentials as they approach the uniform regime. Our results show that quartic traps display a behavior similar to quadratic ones, yet locally at the center of the traps the bulk transition has enhanced critical fluctuations in comparison to the quadratic case. Therefore quartic traps provide a better prerequisite for the experimental observation of true quantum criticality of ultracold bosonic atoms in optical lattices.

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Section: Introductionmentioning

confidence: 99%

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

et al. 2006

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“…In higher dimensional bosonic systems supersolids exist, but they have not been observed in one-dimensional systems so far 18 . Recently a normal phase (scenario c) was found in a numerical study of the one-dimensional Quantum-Phase model 4 , which is the high density limit of the Bose-Hubbard model.…”

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Phases of the one-dimensional Bose-Hubbard model

1998

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The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearestneighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.PACS numbers: 05.30. Jp, 05.70.Jk, 67.40.Db Quantum phase transitions in strongly correlated systems have attracted a lot of interest in recent years. Usually the basic particles are electrons, but in some interesting cases the relevant particles are not fermions but bosons. Examples of experimental systems with superfluid and insulating phases are Cooper pairs in thin granular superconducting films 1 and cooper pairs or fluxes in Josephson junction arrays 2 . While in dimensions greater than one the existence of supersolids 3 , i.e. phases with simultaneous superfluid and crystalline order, has been established in theoretical work, the situation in one dimension is less clear. Recently normal phases that are neither crystalline nor superfluid have been found in a one-dimensional model of Josephson junction arrays 4 in the region where supersolids are found in higher dimensions. In this paper we will verify whether supersolids or normal phases exist in the more general Bose-Hubbard model in one dimension.The Bose-Hubbard model contains the basic physics of interacting bosons on a lattice. It is a minimal bosonic many-particle model that cannot be reduced to a single particle model. The bosons have repulsive interactions, and they can gain energy by hopping to neighboring sites on the lattice. The Hamiltonian with on-site and nearestneighbor interactions iswhere b i are the annihilation operators of bosons on site i,n i = b † i b i the number of particles on site i, t is the hopping matrix element. U and V are on-site and nearestneighbor repulsion, and µ is the chemical potential. The energy scale is set by choosing U = 1.The range of the interactions depends on the individual experimental situation. In general the lattice underlying the system is not an atomic lattice, but a larger structure like a Josephson-junction or a grain in a superconductor. In Josephson-junctions the relevant bosons can be cooper pairs or fluxes, resulting in different interactions.As a starting point we first consider the case of onsite repulsion only. In the (µ, t)-plane Mott-insulating regions are surrounded by the superfluid phase 5 . These phases are separated by two types of phase transitions. On the constant density line the transition is driven by phase fluctuations and is of the Berezinskii-KosterlitzThouless (BKT...

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“…In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid-Mott-insulator transition.The fascinating physics of the superfluid-insulator transition in a system of interacting bosons on a lattice has been attracting constant interest of theorists during recent years [2][3][4][5][6][7][8][9]. Lattice bosons is one of the simplest many-body problems with strong competition between the potential and kinetic energy, and a typical example of the quantum phase transition system.…”

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Revealing the superfluid–Mott-insulator transition in an optical lattice

Kashurnikov¹,

2002

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We study (by an exact numerical scheme) the single-particle density matrix of ∼ 10 3 ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment [1]. In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid-Mott-insulator transition.The fascinating physics of the superfluid-insulator transition in a system of interacting bosons on a lattice has been attracting constant interest of theorists during recent years [2][3][4][5][6][7][8][9]. Lattice bosons is one of the simplest many-body problems with strong competition between the potential and kinetic energy, and a typical example of the quantum phase transition system. One of its great advantages is the possibility to study it by powerful Monte Carlo methods which nowadays allow simulations of many thousands of particles at low temperature with unprecedented accuracy (see, e.g., [9]). However, until very recently the canonical Bose-Hubbard model(where a † i creates a particle on the site i, < ij > stands for the nearest-neighbor sites, n i = a † i a i , and t, U , and µ i , are the hopping amplitude, the on-site interaction, and the on-site external field, respectively) was not particularly useful in the analysis of realistic systems. The situation has changed with the exciting success of the experiment by Greiner et al.[1] (originally proposed by Jaksch et al. [10]) in which a gas of ultracold 87 Rb atoms was trapped in a three-dimensional, simple-cubic optical lattice potential. The uniqueness of the new system is that it is adequately described by the Bose-Hubbard Hamiltonian [10,1], and allows virtually an unlimited control over the strength of the effective interparticle interaction U/t and particle density.The characteristic feature of the experimental setup of Ref.[1] is the presence of the overall parabolic potential V (r) which confines the sample. This feature could be of great advantage if one was able to directly measure the spatial density distribution in the trap. We recall the structure of the µ − U/t phase diagram for the BoseHubbard system [2] which predicts commensurate particle density distribution for the insulating phase whenever the chemical potential lies within the Mott-Hubbard gap. The slowly varying (at the length scale of the lattice period) trapping potential effectively provides a scan over µ of this phase diagram at a fixed value of U/t.Unfortunately, what is measured in the experiment is not the original spatial density distribution in the trap, but the absorption image of the free evolving atomic cloud, after the trapping/optical potential is removed; i.e. the quantity which is directly related to the the singleparticle density matrix in momentum space, ρ kk = n k .[This st...

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Phase transitions in an interacting boson model with near-neighbor repulsion

Cited by 49 publications

References 29 publications

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

Simulations of ultracold bosonic atoms in optical lattices with anharmonic traps

Phases of the one-dimensional Bose-Hubbard model

Revealing the superfluid–Mott-insulator transition in an optical lattice

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