ar X iv : 1 80 2 . 00 12 9 v 1 [ co nd - m at . q ua nt - g as ] 1 F eb 2 01 8 Harmonically Trapped Four - Boson System

Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply-bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body s-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasi-universal, or strongly non-universal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body s-wave scattering length as, as > 0. In the weaklyto medium-stronglyinteracting regime, one of the states approaches the energy obtained for a hard core interaction model. This state is identified as the energetically lowest-lying “BEC state”. Structural properties are also presented.