Universal Properties of Two-Dimensional Boson Droplets

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We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal. In particular, the ratio of the binding energies of (N+1)- and N-boson systems, Bₙ₊₁/Bₙ, approaches a finite limit, approximately 8.567, at large N. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state B₃(0) = 16.522688(1) B₂ and for the excited state B₃(1) = 1.2704091(1) B₂.