大语言模型成功求解三类新型自旋链的贝特方程，发现独特对称性结构。
Bethe Ansatz with a Large Language Model
- 用LLM自动推导积分模型的坐标贝特方程解
- 求得两个新哈密顿量解，其中一例打破左右对称但具PT对称性
- 发现无U(1)不变性的嵌套贝特方程特殊结构，适合广义流体力学应用
我们研究大语言模型（LLM）在数学物理中执行特定计算的能力：求解选定可积自旋链模型的坐标贝特方程解。选取了三个未发表解的可积哈密顿量，其中两个为新模型。实验中，LLM在所有情况下半自主完成任务，偶有错误，经研究人员修正后结果准确。通过独立程序进行精确对角化验证，且作者人工复核了推导过程。所得贝特方程解本身具有意义：第二个模型明显破坏左右对称性，但具备PT对称性，其解对广义流体力学可能具应用价值；第三个模型采用特殊嵌套贝特方程形式，虽存在相互作用，但嵌套层级呈现自由费米子结构，且缺乏U(1)对称性，该结构独特且由LLM首次发现。使用ChatGPT 5.2 Pro与5.4 Pro进行实验。
原文摘要 · Abstract (English)
We explore the capability of a Large Language Model (LLM) to perform specific computations in mathematical physics: the task is to compute the coordinate Bethe Ansatz solution of selected integrable spin chain models. We select three integrable Hamiltonians for which the solutions were unpublished; two of the Hamiltonians are actually new. We observed that the LLM semi-autonomously solved the task in all cases, with a few mistakes along the way. These were corrected after the human researchers spotted them. The results of the LLM were checked against exact diagonalization (performed by separate programs), and the derivations were also checked by the authors. The Bethe Ansatz solutions are interesting in themselves. Our second model manifestly breaks left-right invariance, but it is PT-symmetric, therefore its solution could be interesting for applications in Generalized Hydrodynamics. And our third model is solved by a special form of the nested Bethe Ansatz, where the model is interacting, but the nesting level has a free fermionic structure lacking $U(1)$-invariance. This structure appears to be unique and it was found by the LLM. We used ChatGPT 5.2 Pro and 5.4 Pro by OpenAI.
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