Energy 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

Abstract

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 {\em{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.

14 pages, 13 figures

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Observation of an Efimov spectrum in an atomic system
• Collisional stability of a three-component degenerate Fermi gas
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Observation of universality in ultracold 7Li three-body recombination
• Observation of the Efimov state of the helium trimer
• Universal Properties of the Four-Body System with Large Scattering Length
• Universal properties of a trapped two-component Fermi gas at unitarity
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Efimov physics in bosonic atom-trimer scattering
• Unitary Fermi Gas in a Harmonic Trap
• Energetics and structural properties of three-dimensional bosonic clusters near threshold
• $N$-boson spectrum from a Discrete Scale Invariance
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• Efimov physics and the three-body parameter for shallow van der Waals potentials
• Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics

Cited by in corpus (19)

• Efimov Physics: a review
• Universal few-body physics and cluster formation
• Few-body physics in resonantly interacting ultracold quantum gases
• Universality of an impurity in a Bose-Einstein condensate
• Effective Field Theory for Few-Boson Systems
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Ground-state properties of unitary bosons: from clusters to matter
• Clustering of Four-Component Unitary Fermions
• Quantum unbinding near a zero temperature liquid-gas transition
• Harmonically Trapped Four-Boson System
• Three and four identical fermions near the unitary limit
• Tetramer Bound States in Heteronuclear Systems
• Three-boson spectrum in the presence of 1D spin-orbit coupling: Efimov's generalized radial scaling law
• Les Houches Lectures on Effective Field Theories for Nuclear and (some) Atomic Physics
• Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity
• Energetics and structural properties of two- and three-boson systems in the presence of 1D spin-orbit coupling
• Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach
• Van der Waals five-body size-energy universality
• Few-boson system with a single impurity: Universal bound states tied to Efimov trimers