ORIGINAL RESEARCH article
Front. Phys.
Sec. Nuclear Physics
Exact Bethe Ansatz for the Vibron Model: A critical reassessment of q-deformation and parameterization
Provisionally accepted
- Zhejiang Sci-Tech University, Hangzhou, China
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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 tech-niques, 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.
Keywords: Bethe ansatz equation, Dynamical symmetry group, q-deformation, quantum phase transitions (QPT), Vibron Model
Received: 20 Nov 2025; Accepted: 07 Jan 2026.
Copyright: © 2026 Jalili, Saleki and Chen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Amir Jalili
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