Quantum criticality and stability of three-body Coulomb systems

We present quantum phase transitions and critical phenomena of three-body Coulomb systems with charges $(Q,$ q, $Q)$ and masses $(M,$ m, $M).$ Full numerical results, using the finite-size scaling method, for an arbitrary mass ratio 0<~κ=(1+m/M)^-1<~1 over the range 1<~λ=|Q/q|<~1.25, show that there exists a transition curve λc(κ) through which all systems undergo a first-order phase transition from stable to unstable. Particularly, λc(κ) has a minimum at κₘ=0.35, which leads to a new proposed classification of the three-body Coulomb systems: moleculelike systems, κ>κₘ, such as Ps^- (κ=0.5) and atomlike systems, κ<κₘ, such as p̄p̄d (κ=0.33).