Integrability from a single conservation law in quantum spin chains
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912867865853952 |
|---|---|
| author | Hokkyo, Akihiro |
| author_facet | Hokkyo, Akihiro |
| contents | We prove that for translationally invariant quantum spin chains with finite-range interactions, the existence of a specific conservation law known as the Reshetikhin condition implies the presence of infinitely many local conserved quantities, i.e., integrability. This shows that the entire hierarchy of conservation laws associated with solutions of the Yang--Baxter equation is already encoded in the lowest nontrivial conservation law. Combined with recent rigorous results on nonintegrability, our theorem strongly restricts the possibility of partially integrable systems that admit only a finite but large number of local conserved quantities. Our work establishes a rigorous foundation for the systematic identification of new integrable models and deepens the algebraic understanding of conservation-law structures in quantum spin chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrability from a single conservation law in quantum spin chains Hokkyo, Akihiro Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics We prove that for translationally invariant quantum spin chains with finite-range interactions, the existence of a specific conservation law known as the Reshetikhin condition implies the presence of infinitely many local conserved quantities, i.e., integrability. This shows that the entire hierarchy of conservation laws associated with solutions of the Yang--Baxter equation is already encoded in the lowest nontrivial conservation law. Combined with recent rigorous results on nonintegrability, our theorem strongly restricts the possibility of partially integrable systems that admit only a finite but large number of local conserved quantities. Our work establishes a rigorous foundation for the systematic identification of new integrable models and deepens the algebraic understanding of conservation-law structures in quantum spin chains. |
| title | Integrability from a single conservation law in quantum spin chains |
| topic | Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2508.20713 |