Quantum criticality at the large‐dimensional limit: Three‐body Coulomb systems

Abstract

AbstractWe 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=½, 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, 2001