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

TL;DR

This paper introduces a method to construct unitary Yang-Baxter R matrices with an 'X' form, enabling the generation of entangled states and the development of a Yang-Baxter Hamiltonian with Yangian symmetry, advancing quantum integrable systems.

Contribution

It provides a novel construction of unitary Yang-Baxter R matrices with an 'X' form and explores their role in generating entangled states and Yangian symmetry in quantum systems.

Findings

Constructed 'X' form unitary Yang-Baxter R matrices.

Generated entangled states in high-dimensional systems.

Developed a Yang-Baxter Hamiltonian with Yangian symmetry.

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 $(2j_{1}+1)\times (2j_{2}+1)$-dimensional system with these Yang-Baxter $\breve{R}$ matrices. By means of Yang-Baxter approach, a $8\times 8$ Yang-Baxter Hamiltonian is constructed. Yangian symmetry and Yangian generators as shift operators for this Yang-Baxter system are investigated in detail.