Bethe Ansatz with a Large Language Model

TL;DR

This paper demonstrates that large language models can autonomously compute complex Bethe Ansatz solutions for new integrable spin chain models, with minimal human correction, verified against exact methods.

Contribution

The study shows LLMs can independently derive novel Bethe Ansatz solutions for integrable models, including those with unique structures, advancing AI's role in mathematical physics research.

Findings

LLMs successfully solved three integrable models, two of which are new.

Solutions were verified against exact diagonalization and manual checks.

LLMs identified unique nested Bethe Ansatz structures without prior knowledge.

Abstract

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 We select three integrable Hamiltonians for which the solutions were unpublished; two of the Hamiltonians are actually new.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.