One-dimensional Bose gas in optical lattices of arbitrary strength

Astrakharchik, G. E.; Krutitsky, K. V.; Lewenstein, Maciej; Mazzanti, F.

doi:10.1103/physreva.93.021605

Cited by 36 publications

(38 citation statements)

References 40 publications

(65 reference statements)

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“…Using the condition K TL = 1/2 (see section 8.1), one can determine the critical value of J/U for the transition from the superfluid into the Mott insulator. Calculations ofS 0 (k) by exact diagonalization for chains up to L = 14 sites give (J/U ) c ≈ 0.28 [366] in perfect agreement with other calculations based on the exact diagonalization listed in Table 1. The parity correlations are of the same order of magnitude as the particle-number correlations.…”

Section: Higher-order Correlation Functionssupporting

confidence: 85%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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Section: Higher-order Correlation Functionssupporting

confidence: 85%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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“…Dashed line, uniform density limit, Eq. (39). The peaks at commensurate momentum k = qkL, q = 1, 2, · · · are macroscopically large and are denotes with arrows and the trivial peak Sρ(0) = N is not shown.…”

Section: Discussion Of Numerical Resultsmentioning

confidence: 99%

Optical lattices as a tool to study defect-induced superfluidity

et al. 2017

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We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides a extremely well-controlled model for studying defect-induced superfluidity.

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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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confidence: 99%

“…Consistently with the use of periodic boundary conditions, it is understood thatĉ † L+1,σ =ĉ † 1,σ (ĉ L+1,σ =ĉ 1,σ ). The hopping energy t and the on-site interaction parameter U can be computed from Wannier functions integrals [17,34] following the standard procedure [27]. The zero-temperature equation of state of the Hubbard model (2) was first determined by Lieb and Wu [3] using the Bethe Ansatz technique [35].…”

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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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One-dimensional Bose gas in optical lattices of arbitrary strength

Cited by 36 publications

References 40 publications

Ultracold bosons with short-range interaction in regular optical lattices

Ultracold bosons with short-range interaction in regular optical lattices

Optical lattices as a tool to study defect-induced superfluidity

One-dimensional repulsive Fermi gas in a tunable periodic potential

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