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

Qicun Shi, Sabre Kais

Research output: Contribution to journalConference article

9 Citations (Scopus)


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 = 1/2, 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.

Original languageEnglish
Pages (from-to)307-314
Number of pages8
JournalInternational Journal of Quantum Chemistry
Issue number4-5
Publication statusPublished - 15 Nov 2001
EventInternational Symposium on Atomic, Molecular and Condensed Matter Theory - St.Augustine, FL, United States
Duration: 24 Feb 20012 Mar 2001



  • ABA Coulomb system
  • Atom-like region
  • Hamiltonian
  • Molecule-like region
  • Reference particle
  • Zero angular correlation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

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