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 $\sim p^{-1/3}$ 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 $a_{-}(N)\sim N^{-1/2}$ 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.

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