Yang-Baxter $${\breve R}$$ matrix, entanglement and Yangian

Abstract

We present a method to construct “X” form unitary Yang-Baxter \({\breve R}\) matrices, which act on the tensor product space \({V_{i}^{j_{1}}\otimes V_{i+1}^{j_{2}}}\) . We can obtain a set of entangled states for (2j 1 + 1) × (2j 2 + 1)-dimensional system with these Yang-Baxter \({\breve R}\) matrices. By means of Yang-Baxter approach, a 8 × 8 Yang-Baxter Hamiltonian is constructed. Yangian symmetry and Yangian generators as shift operators for this Yang-Baxter system are investigated in detail.