Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations

The ground state and structure of a one-dimensional Bose gas with dipolar repulsions is investigated at zero temperature by a combined Reptation Quantum Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid behavior emerges in a wide range of intermediate densities, evolving into a Tonks-Girardeau gas at low density and into a classical quasi-ordered state at high density. The density dependence of the Luttinger exponent is extracted from the numerical data, providing analytical predictions for observable quantities, such as the structure factor and the momentum distribution. We discuss the accessibility of such predictions in current experiments with ultracold atomic and molecular gases. More recent experiments have demonstrated that the range of the interactions can also be manipulated. Dipole interactions with long-range anisotropic character have been observed in 52 Cr atoms [7] after exploiting the large magnetic moments of this atomic species, that is µ d ≈ 6µ B with µ B being the Bohr magneton. A BEC containing up to 50000 52 Cr atoms has then been obtained below a transition temperature T c ≃ 700nK [8] and its dynamical behavior is being investigated [9]. Promising proposals to tune and shape the dipolar interaction strength in quantum gasees of heteronuclear polar molecules have more recently been suggested [10]. Significant theoretical predictions have accompanied such realizations [11]. The stability diagram of anisotropic confined dipolar gases has been predicted to be governed by the trapping geometry [12,13], as corroborated by Path-Integral QMC studies [14]. Different conclusions are reached by more recent Diffusion QMC simulations including the dependence of a on the dipole interaction [15]. PACSTuning of the interactions can be combined with the enhancement of quantum fluctuations after reducing their dimensionality by e.g. storing them in elongated traps [16,17], which could be relevant to applications such as precision measurements [18], quantum computing [19], atomtronic quantum devices, and theoretical investigations of novel quantum phase transitions [20].In the case of quasi one-dimensional (1D) condensates with short-range interactions, a rich phenomenology is known to emerge from the collective character of the single-particle degrees of freedom, despite the absence of broken symmetries [21]. Bosons are known to arrange in a Luttingerliquid state, with single particles being replaced by collective density excitations [22,23]. Strong repulsion may also lead to the fermionization of interacting bosons in the so-called Tonks-Girardeau (TG) regime [24,25,26]. Experiments in elongated traps have provided evidence for such 1D fluctuations [16].In the case of quasi-1D condensates with dipolar interactions, an interesting question arises whether the quantum fluctuations are sufficiently enhanced to drive the BEC in a strong-coupling regime. More recent Diffusion QMC simulations [27] for a homogeneous 1D dipolar Bose gas have revealed a crossover behavior with increasing li...

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“…We reach this conclusion by comparing theoretical results from a bosonization approach against Reptation Quantum Monte Carlo simulations [28]. By…”

Section: Pacsmentioning

confidence: 99%

Evidence of Luttinger-liquid behavior in one-dimensional dipolar quantum gases

et al. 2007

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“…For quantities that do not commute with the Hamiltonian, we use Reptation Monte Carlo [18] with the bounce algorithm [19]. We sample the path distribution…”

Section: B Projector Monte Carlomentioning

confidence: 99%

QWalk: A quantum Monte Carlo program for electronic structure

Wagner

Bajdich

Mitáš

2009

Journal of Computational Physics

160

140

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“…The LRDMC and the DMC methods have the same efficiency for small Z, although it is possible to have a gain in the LRDMC efficiency by an ad hoc choice of the kinetic parameters, particularly for heavier elements. We conclude, by noting that the same Green function presented here can be used in the Reptation Quantum Monte Carlo method [16]. This work was supported by the NSF grant DMR-0404853.…”

mentioning

confidence: 99%

Beyond the locality approximation in the standard diffusion Monte Carlo method

2006

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We present a way to include non local potentials in the standard Diffusion Monte Carlo method without using the locality approximation. We define a stochastic projection based on a fixed node effective Hamiltonian, whose lowest energy is an upper bound of the true ground state energy, even in the presence of non local operators in the Hamiltonian. The variational property of the resulting algorithm provides a stable diffusion process, even in the case of divergent non local potentials, like the hard-core pseudopotentials. It turns out that the modification required to improve the standard Diffusion Monte Carlo algorithm is simple.PACS numbers: 02.70. Ss, 31.10.+z, Diffusion Monte Carlo (DMC) is one of the most successful methods to compute the ground state properties of quantum systems. Although the fixed node (FN) approximation is needed to cure the infamous sign problem for fermions, the accuracy of the DMC framework has yielded many benchmark results [1]. However, when the DMC method is applied to "ab initio" realistic Hamiltonians, its computational cost scales ∝ Z 6.5 , where Z is the atomic number [2]. Therefore, the use of pseudopotentials is necessary to make those calculations feasible.Since the pseudopotentials are usually non local, the "locality approximation" is made besides the FN, by replacing the true Hamiltonian H with an effective one H eff , which reads[3]:

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Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations

Cited by 211 publications

References 16 publications

Evidence of Luttinger-liquid behavior in one-dimensional dipolar quantum gases

Evidence of Luttinger-liquid behavior in one-dimensional dipolar quantum gases

QWalk: A quantum Monte Carlo program for electronic structure

Beyond the locality approximation in the standard diffusion Monte Carlo method

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