Incorporating exact two-body propagators for zero-range interactions into<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-body Monte Carlo simulations

Yan, Yangqian; Blume, D.

doi:10.1103/physreva.91.043607

Cited by 20 publications

(29 citation statements)

References 78 publications

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“…To calculate the N -boson energy for the Hamiltonian with interaction model 2bZR+3bRp, we apply the PIMC technique [25,47]. The PIMC technique is an, in principle, exact finite-temperature method; the errors, which originate from the discretization of the imaginary time and the stochastic evaluation of integrals, can be reduced systematically.…”

Section: N -Body Results At Unitarity For the Model 2bzr+3brpmentioning

confidence: 99%

“…This requirement corresponds to |E N | ≫ ω. Since the density of states of the harmonically trapped center of mass pseudoparticle is known analytically, the ground state energy E N of the N -boson droplet in free space can be extracted from the finite-temperature energy [25,28].…”

Section: N -Body Results At Unitarity For the Model 2bzr+3brpmentioning

confidence: 99%

“…Our work considers the N -body ground state using a novel Monte Carlo approach [25] that allows for the treatment of two-body zero-range interactions. The Monte Carlo approach can unfortunately not treat three-body zero-range interactions, i.e., it is not capable of treating the Hamiltonian 2bZR+3bZR.…”

Section: Introductionmentioning

confidence: 99%

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Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Yan

Blume

2015

Phys. Rev. A

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arXiv:1508.00081v1 [cond-mat.quant-gas] 1 Aug 2015Energy and structural properties of N-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator The low-energy spectrum of N -boson clusters with pairwise zero-range interactions is believed to be governed by a three-body parameter. We study the ground state of N -boson clusters with infinite two-body s-wave scattering length by performing ab initio Monte Carlo simulations. To prevent Thomas collapse, different finite-range three-body regulators are used. The energy and structural properties for the three-body Hamiltonian with two-body zero-range interactions and three-body regulator are in much better agreement with the "ideal zero-range Efimov theory" results than those for Hamiltonian with two-body finite-range interactions. For larger clusters we find that the ground state energy and structural properties of the Hamiltonian with two-body zero-range interactions and finite-range three-body regulators are not universally determined by the three-body parameter, i.e., dependences on the specific form of the three-body regulator are observed. For comparison, we consider Hamiltonian with two-body van der Waals interactions and no three-body regulator. For the interactions considered, the ground state energy of the N -body clusters is-if scaled by the three-body ground state energy-fairly universal, i.e., the dependence on the short-range details of the two-body van der Waals potentials is small. Our results are compared with the literature.

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Section: N -Body Results At Unitarity For the Model 2bzr+3brpmentioning

confidence: 99%

Section: N -Body Results At Unitarity For the Model 2bzr+3brpmentioning

confidence: 99%

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Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Yan

Blume

2015

Phys. Rev. A

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“…We include zero-range unitary interactions between two bosons through the exact two-body propagator [24,25], and treat them with a highly efficient direct-sampling approach [15]. The many-body density matrix is then built via the pair-product approximation.…”

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confidence: 99%

Momentum Distribution in the Unitary Bose Gas from First Principles

Comparin

Krauth

2016

Phys. Rev. Lett.

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We consider a realistic bosonic N -particle model with unitary interactions relevant for Efimov physics. Using quantum Monte Carlo methods, we find that the critical temperature for BoseEinstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.First predicted in 1970[1], the Efimov effect describes the behavior of three strongly interacting bosons when any two of them cannot bind. At unitarity, when the scattering length diverges, the three-body bound states are scale invariant and they form a sequence up to vanishing binding energy and infinite spatial extension. Efimov trimers had been intensely discussed in nuclear physics, but it was in an ultracold gas of caesium atoms that they were finally discovered [2]. To observe Efimov trimers, experiments in atomic physics rely on Feshbach resonances [3], which permits to instantly switch a gas between weak interactions and the unitary limit. Such a control of interactions lacks in nuclear physics or condensed matter experiments, and singular interactions can be probed there only in the presence of accidental fine tuning [4]. Beyond the original system[2], Efimov trimers have now been observed for several multi-component systems, including bosonic, fermionic and Bose-Fermi mixtures [5][6][7]. These experimental findings are interpreted in terms of the theory of few-body strongly interacting quantum systems. For three identical bosons in three dimensions, a complete universal theory is available, on and off unitarity [4]. Further theoretical work is aimed at understanding bound states for more than three bosons, mixtures, and the effects of dimensionality.Near-unitary interparticle interactions also impact the thermodynamics of the atomic gas, the description of which presents a challenge beyond the traditional theory of the Efimov effect. In addition, mean-field theory does not apply to infinite interactions [8], and the virial expansion [9] fails to describe the low-temperature state. Moreover, in atomic-physics experiments, strong interactions enhance the three-body loss rate, making the gas of bosons unstable. A characterization of the universal dynamics of these losses has been recently achieved [10][11][12]. On the other hand, a single breakthrough experiment [13] has addressed the low-temperature thermodynamics for a unitary bosonic gas, coming to the conclusion that equilibrium was approached faster than the system life-time. The importance of this system stems from its univer...

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“…In the present work, we have resorted to the well-established pair product approximation [4,40,41]. In the light of the representation (9), the PIGS estimators of F (q, τ ) takes the form…”

Section: The Pigs Methodsmentioning

confidence: 99%

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

et al. 2016

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We compute several groundstate properties and the dynamical structure factor of a 0-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path-integral ground-state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of groundstate properties and collective excitations of 2D-SC and 4 He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in 4 He. This result is in contrast with the view that the roton is the soft mode of the fluid-solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short range order as quantified by the height of the first peak of the static structure factor.

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Incorporating exact two-body propagators for zero-range interactions intoN-body Monte Carlo simulations

Cited by 20 publications

References 78 publications

Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

Momentum Distribution in the Unitary Bose Gas from First Principles

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

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