Complete classification of integrability and nonintegrability for spin- 1 2 chain with symmetric nearest-neighbor interaction
Abstract
General spin- 1 2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are nonintegrable in the sense that they possess no nontrivial local conserved quantities. This result confirms that there are no missing integrable systems; i.e., integrable systems in this class are exactly those that are already known. In addition, this result excludes the possibility of intermediate systems that have a finite number of nontrivial local conserved quantities. Our findings support the expectation that integrable systems are exceptional in quantum many-body systems and most systems are nonintegrable.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Algebraic structures and combinatorial models
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Physical Review Research
- Publisher
- American Physical Society (APS)
- Volume
- 8
- Issue
- 3
- Publication date
- 9 June 2026
- Language
- EN