A Simple Necessary and Sufficient Condition for Yang--Baxter Integrability
- Published
- Source
- arXiv
- Paper number
- 792
- Field
- Research
- arXiv ID
- 2607.29660
Key points
- It gives a rigorous proof, for translation-invariant nearest-neighbor spin chains, of a conjecture that had been open for 40 years: that the Reshetikhin condition is necessary and sufficient for Yang-Baxter integrability.
- The condition can be checked directly at the Hamiltonian level and is equivalent to conservation of the total energy flow, so it is also experimentally observable.
- It establishes a quantum version of the Liouville-Arnold theorem, showing that Yang-Baxter integrability is equivalent to the existence of infinitely many local conservation laws.
- When searching for new integrable models, one can check the Hamiltonian directly instead of finding an R-matrix, which greatly simplifies the search.
Paper links
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