Quantum criticality and stability of three-body Coulomb systems

Abstract

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 $0<~\ensuremath{\kappa}{=(1+m/M)}^{\ensuremath{-}1}<~1$ over the range $1<~\ensuremath{\lambda}=|Q/q|<~1.25,$ show that there exists a transition curve ${\ensuremath{\lambda}}_{c}(\ensuremath{\kappa})$ through which all systems undergo a first-order phase transition from stable to unstable. Particularly, ${\ensuremath{\lambda}}_{c}(\ensuremath{\kappa})$ has a minimum at ${\ensuremath{\kappa}}_{m}=0.35,$ which leads to a new proposed classification of the three-body Coulomb systems: moleculelike systems, $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{m},$ such as ${\mathrm{Ps}}^{\ensuremath{-}}$ $(\ensuremath{\kappa}=0.5)$ and atomlike systems, $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{m},$ such as $\overline{p}\overline{p}d$ $(\ensuremath{\kappa}=0.33).$