Exact Bethe Ansatz for the vibron model: a critical reassessment of q-deformation and parameterization
FRONTIERS IN PHYSICS, vol.14, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14
- Publication Date: 2026
- Doi Number: 10.3389/fphy.2026.1750902
- Journal Name: FRONTIERS IN PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
The vibron model classifies energy spectra through U ( n ) -> SO ( n ) irreducible representation (irrep) branching, enabling exploration of quantum phase transitions between vibrational and rotational regimes. We advance a solvable Bethe Ansatz framework, deriving exact solutions for the vibron Hamiltonian and addressing discrepancies in prior studies. By applying algebraic techniques, we demonstrate that precise control parameters-rather than q -deformation-are essential for accurate spectral predictions. This study critically reassesses existing computational methods, emphasizing parameter optimization to improve alignment with experimental data. Our refined approach accurately reproduces the procedure for obtaining reproducible molecular energy spectra, elucidating the impact of control parameters on quantum phase transitions.