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

TL;DR

This study investigates the properties of N-boson clusters with zero-range interactions, emphasizing the role of three-body regulators, and finds that while energies scale universally with three-body energies, structural properties depend on the regulator form.

Contribution

The paper provides ab initio Monte Carlo analysis of N-boson clusters with zero-range interactions, highlighting the influence of three-body regulators on energy and structure, and compares with van der Waals interactions.

Findings

Zero-range models with three-body regulators align well with Efimov theory.

Ground state energies show near universality when scaled by three-body energies.

Structural properties depend on the specific form 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.