Quantum criticality at the large-dimensional limit: Three-body coulomb systems

摘要

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 lambda = Q/q and k = [1 + (m/M)](-1). The system exhibits critical points with mean field critical exponents (alpha = 0, beta = 1/2, delta = 3, gamma = 1). We calculate the critical curve lambda (c) (kappa) 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 --> infinity limit is a convex function of kappa 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. (C) 2001 John Wiley & Sons, Inc. [References: 34]