Two-level interacting boson models beyond the mean field

Abstract

The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.

14 pages, 13 figures

References in corpus (8)

• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing
• Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics
• Thermodynamic analogy for quantum phase transitions at zero temperature
• A scalar two-level boson model to study the IBM phase diagram in the Casten triangle
• Continuous unitary transformations in two-level boson systems
• Finite-size scaling exponents in the interacting boson model
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model

Cited by in corpus (13)

• Excited state quantum phase transitions in many-body systems
• Quantum phase transitions in the interacting boson model
• Decoherence as a signature of an excited state quantum phase transition
• Decoherence due to an excited state quantum phase transition in a two-level boson model
• Microscopic Analysis of Order Parameters in Nuclear Quantum Phase Transitions
• Dual algebraic structures for the two-level pairing model
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Non-thermal quantum phase transitions
• Emergent quantum phases in a heteronuclear molecular Bose--Einstein condensate model
• Phenomenological and microscopic cluster models I. The geometric mapping
• On the relation between $E(5)-$models and the interacting boson model
• Relationship between X(5)-models and the interacting boson model
• Scaling Properties of the Lipkin Model at the Critical Point