R-matrices for integrable $SU(2)\times U(1)$-symmetric S=1/2 spin-orbital chains

TL;DR

This paper presents the classification of new R-matrices solving the Yang-Baxter equation for $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chains, revealing models relevant to various condensed matter systems.

Contribution

The author developed a specialized computer algorithm to find and classify 8 new R-matrices for the Yang-Baxter equation in this context, expanding the set of integrable models.

Findings

Presented 8 new R-matrices grouped into 5 classes.

Identified integrable models related to real physical systems.

Provided explicit solutions relevant to condensed matter physics.

Abstract

The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained integrable models there are special cases related to 1D ferromagnet ${\rm TDAE-C}_{60}$, 1D superconductors ${\rm AC}_{60}$ (A=K, Cs, Rb), the quarter filled ladder compound ${\rm NaV}_2{\rm O}_5$ and the model of correlated electrons on a chain of Berry phase molecules.