Yang-Baxter and the Boost: splitting the difference

TL;DR

This paper advances the classification of Yang-Baxter equation solutions by applying a boost operator method to find all non-difference form solutions for spin chains with small local Hilbert spaces, revealing new solutions.

Contribution

It extends the classification of Yang-Baxter solutions using the boost operator method to non-difference form cases and provides a comprehensive classification for certain symmetric spin chains.

Findings

Classified all 16x16 solutions with su(2)⊕su(2) symmetry.

Identified solutions including the Hubbard model and AdS5×S5 superstring S-matrix.

Discovered novel Yang-Baxter solutions in the process.

Abstract

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all $16\times 16$ solutions which exhibit $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$ symmetry, which include the one-dimensional Hubbard model and the $S$-matrix of the ${\rm AdS}_5 \times {\rm S}^5$ superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.