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Springer monographs in mathematics

Models of Zero-Range Interaction for the Bosonic Trimer at Unitarity

Matteo Gallone, Alessandro Michelangeli

Published Jul 5, 2022• 1 citation
Publisher
DOI
10.1007/978-3-031-10885-3_6

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•Jun 16, 2021•1 citation
We investigate the appearance of a four-boson limit cycle in Hamiltonian systems at the unitarity limit. The model interaction incorporates two-, three-, and four-body short-range potentials, which allow us to disentangle the interwoven dynamics of three- and four-boson energy levels. Through numerical evidence, we observe a correlation between the energies of two successive universal tetramer levels for a fixed weakly bound trimer, which is found to be largely model independent. Interestingly, this correlation cycle is consistent with the findings of Hadizadeh et al. [Phys. Rev. Lett. 107, 135304 (2011)] using a zero-range model.
We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two- and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parametrization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited.
We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two- and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parameterization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground-states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited.