Mott transition for strongly interacting one-dimensional bosons in a shallow periodic potential

Boéris, Guilhem; Gori, Lorenzo; Hoogerland, M. D.; Kumar, Avinash; Lucioni, Eleonora; Tanzi, L.; Inguscio, M.; Giamarchi, Thierry; D’Errico, Chiara; Carleo, Giuseppe; Modugno, Giovanni Carlo; Sanchez-Palencia, Laurent

doi:10.1103/physreva.93.011601

Cited by 57 publications

(85 citation statements)

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“…Recently, a new experimental study [39] of the phase diagram by the LENS group in Florence appeared, in particular, analyzing shallow lattices where we find a discrepancy with the sine-Gordon model and the transport measurements of Ref. [24].…”

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confidence: 99%

One-dimensional Bose gas in optical lattices of arbitrary strength

et al. 2016

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One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated, and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate. DOI: 10.1103/PhysRevA.93.021605 The Bose-Hubbard model (BHM) was introduced in 1963 [1,2]. While the original motivation was to describe a crystalline solid, for which the model failed, the BHM became one of the fundamental quantum many-body problems. It has found clear-cut realization with ultracold atoms in deep optical lattices. This led to the seminal observation [3] of the superfluidMott-insulator quantum phase transition [4] following the proposal of Ref. [5]. In many aspects the experiments surpass the theory as shallow optical lattices can be easily realized, while an exact quantum many-body description of such systems is lacking. Even the case of deep optical lattices is controversial, as the scattered discussions demonstrate [6][7][8][9][10][11], indicating the necessity to go beyond the standard BHM (for a review, see Ref. [12]). Nevertheless, the BHM is commonly used for lattice systems in different dimensions and it frequently works very well. Still, there arise natural and important questions that have motivated the present work: When can it be used with confidence? What is the regime of validity of the BHM?The discrete BHM is derived from a continuous space model that, due to its complexity, has only been addressed recently [13][14][15][16][17][18]. In this Rapid Communication, we use the exact diffusion quantum Monte Carlo method [13,15,[19][20][21] and investigate one-dimensional Bose gas in optical lattices using a continuous Hamiltonian in real space. We compare the results with those obtained from the BHM and determine its regions of validity. Furthermore, a whole new generation of clean experiments on one-dimensional Bose gases loaded in optical lattices [22,23] have appeared, while the comparison of theory with experiment is not perfect [24,25]. We also analyze the sine-Gordon (SG) model, commonly used for shallow lattices [9,26,27], and show that it cannot be straightforwardly used to predict the position of the phase transition and the value of the gap [24]. We calculate the static structure factor, the one-body density matrix, the energy gap, and the Luttinger parameter and its dependence on the interaction and lattice strengths. Finally, we compare our results with the experiments of Ref.[24]-surprisingly, our theory, which is in principle superior to all approximate ones, does not always provide a better description.The first quant...

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One-dimensional Bose gas in optical lattices of arbitrary strength

et al. 2016

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“…Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the interaction strength can be captured only via multi-band or continuous-space models. Recent theoretical and experimental studies have addressed the regime of shallow OLs and strong interactions, investigating intriguing phenomena such as Mott and pinning bosonic localization transitions [14][15][16][17][18], Anderson localization [19][20][21], Bose-Glass phases [22], and itinerant ferromagnetism [23,24].…”

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One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

Phys. Rev. A

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By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

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“…However, the lattice setup with a rational number λ 1 /λ 2 is not very common and deserves therefore an investigation, particularly due to the likelihood that there may be not much difference between the use of a rational and irrational λ 1 /λ 2 . The same argument has been made recently by Boeris et al [16] who stated (quoting them): "... it is not necessary to implement truly irrational numbers with mathematical (i.e., unattainable) precision; after all, on a finite lattice one can "resolve" only a finite number of digits." In fact, real disorder can only be achieved by a speckle potential and the investigation of bosons in this kind of potential, and add to this a quasidisordered one, has been going on intensively in the last few years [11,18,20,22,.…”

Section: Introductionmentioning

confidence: 73%

“…The current results are also in line with Edwards et al [66] who demonstrated that the effects of weak perturbations to a primary 1D OL disappear as interactions get stronger and we are in the strongly interacting regime. During the preparation of this paper, we learnt of an in-vestigation bearing similarities to ours by Boéris et al [16] where, among other issues, the WA has been applied to reproduce the SG transition, except that they only use a periodic OL with a different procedure than ours here. Fig.…”

Section: Discussionmentioning

confidence: 99%

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Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

Sakhel

2016

Phys. Rev. A

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The sensitivity of the Sine-Gordon (SG) transition of strongly interacting bosons confined in a shallow, one-dimensional (1D), periodic optical lattice (OL), is examined against perturbations of the OL. The SG transition has been recently realized experimentally by Haller et al. [Nature 466, 597 (2010)] and is the exact opposite of the superfluid (SF) to Mott insulator (MI) transition in a deep OL with weakly interacting bosons. The continuous-space worm algorithm (WA) Monte Carlo method [Boninsegni et al., Phys. Rev. E 74, 036701 (2006)] is applied for the present examination. It is found that the WA is able to reproduce the SG transition which is another manifestation of the power of continuous-space WA methods in capturing the physics of phase transitions. In order to examine the sensitivity of the SG transition, it is tweaked by the addition of the secondary OL. The resulting bichromatic optical lattice (BCOL) is considered with a rational ratio of the constituting wavelengths λ1 and λ2 in contrast to the commonly used irrational ratio. For a weak BCOL, it is chiefly demonstrated that this transition is robust against the introduction of a weaker, secondary OL. The system is explored numerically by scanning its properties in a range of the Lieb-Liniger interaction parameter γ in the regime of the SG transition. It is argued that there should not be much difference in the results between those due to an irrational ratio λ1/λ2 and due to a rational approximation of the latter, bringing this in line with a recent statement by Boéris et al. [Phys. Rev. A 93, 011601(R) (2016)]. The correlation function, Matsubara Green's function (MGF), and the single-particle density matrix do not respond to changes in the depth of the secondary OL V1. For a stronger BCOL, however, a response is observed because of changes in V1. In the regime where the bosons are fermionized, the MGF reveals that hole excitations are favored over particle excitatons manifesting that holes in the SG regime play an important role in the response of properties to changes in γ.

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Mott transition for strongly interacting one-dimensional bosons in a shallow periodic potential

Cited by 57 publications

References 57 publications

One-dimensional Bose gas in optical lattices of arbitrary strength

One-dimensional Bose gas in optical lattices of arbitrary strength

One-dimensional repulsive Fermi gas in a tunable periodic potential

Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the pinning transition: A worm-algorithm Monte Carlo study

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