### Abstract

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 λ_{c}(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 language | English |
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Pages (from-to) | 307-314 |

Number of pages | 8 |

Journal | International Journal of Quantum Chemistry |

Volume | 85 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - 15 Nov 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

**Quantum criticality at the large-dimensional limit : Three-body Coulomb systems.** / Shi, Qicun; Kais, Sabre.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 85, no. 4-5, pp. 307-314. https://doi.org/10.1002/qua.1542

}

TY - JOUR

T1 - Quantum criticality at the large-dimensional limit

T2 - Three-body Coulomb systems

AU - Shi, Qicun

AU - Kais, Sabre

PY - 2001/11/15

Y1 - 2001/11/15

N2 - 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.

AB - 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.

KW - ABA Coulomb system

KW - Atom-like region

KW - Hamiltonian

KW - Molecule-like region

KW - Reference particle

KW - Zero angular correlation

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U2 - 10.1002/qua.1542

DO - 10.1002/qua.1542

M3 - Article

VL - 85

SP - 307

EP - 314

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 4-5

ER -