Quantum-unbinding near a zero temperature liquid-gas transition

We discuss the quantum phase transition from a liquid to a gaseous ground state in a Bose fluid with increasing strength of the zero point motion. It is shown that in the zero pressure limit, the two different ground states are separated by a quantum tricritical point whose position is determined by a vanishing two-body scattering length. In the presence of a finite three-body scattering amplitude, the superfluid gas at this point exhibits sound modes whose velocity scales linearly with density while the compressibility diverges ∼p^-1/3 in the limit of vanishing pressure p. In the liquid regime of negative scattering lengths, it is shown that N-body bound states exist up to arbitrary N, consistent with a theorem by Seiringer. The asymptotic scaling of the scattering lengths where they appear from the continuum is determined from a finite size scaling analysis in the vicinity of the quantum tricritical point. This also provides a qualitative understanding of numerical results for the quantum unbinding of small clusters.