Quantum Criticality at the Large-Dimensional Limit: Three-Body Coulomb Systems

We present quantum phase transitions and critical phenomena at the large-dimension (D) limit for three-body ABA Coulomb systems with charges (Q, q, Q) and masses (M, m, M). The Hamiltonian depends linearly on two parameters λ = |Q/q| and κ = [1 + (m/M)]−1. The system exhibits critical points with mean field critical exponents (α = 0, β = 2 , δ = 3, γ = 1). We calculate the critical curve λc(κ) through which all systems undergo a continuous-phase transition from the symmetrical configuration, the two like particles have the same distance from the reference particle, to the unsymmetrical phase. The critical curve at D → ∞ limit is a convex function of κ and very similar to the one obtained at D = 3 with variational calculations. We also calculated the line of zero angular correlation in the mass polarization term, which separates the symmetrical phase to an atom-like region and a molecule-like region. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 85: 307–314, 2001