Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing

Area of Science:

• Quantum mechanics
• Nuclear physics
• Condensed matter physics

Background:

• The interacting boson model (IBM) describes collective states in nuclei.
• Understanding quantum phase transitions (QPTs) is crucial for nuclear structure and dynamics.
• The nature of QPTs in quantum many-body systems remains an active area of research.

Purpose of the Study:

• To elucidate the mechanisms driving quantum phase transitions in the interacting boson model.
• To differentiate the origins of second-order and first-order phase transitions within the IBM.
• To propose a novel model Hamiltonian exhibiting a first-order QPT in finite systems.

Main Methods:

• Analysis of the interacting boson model Hamiltonian.
• Investigation of phase transition orders (first-order vs. second-order).
• Application of concepts like quantum integrability and level repulsion.
• Development of a model Hamiltonian for finite systems.

Main Results:

• The second-order phase transition from U(5) to O(6) is linked to quantum integrability.
• All first-order phase transitions in the model arise from level repulsion.
• A singular point of level crossing is identified as a key feature for first-order transitions.
• A new model Hamiltonian is proposed, demonstrating a true first-order phase transition for finite systems.

Conclusions:

• Quantum integrability and level repulsion are key mechanisms governing QPTs in the IBM.
• The study provides a clear distinction between the origins of different order phase transitions.
• The proposed Hamiltonian offers a new avenue for studying finite-size effects in quantum phase transitions.