Yang-Baxter equation in spin chains with long range interactions

TL;DR

This paper explores the integrability of long-range interacting $su(n)$ spin chains and Calogero-Sutherland models, demonstrating their connection to the Yang-Baxter equation, deriving conserved quantities, and diagonalizing them.

Contribution

It establishes the role of the Yang-Baxter equation in the integrability of these models and provides explicit expressions for conserved quantities and their diagonalization.

Findings

Properties derived from a transfer matrix obeying the Yang-Baxter equation

Explicit expressions for conserved quantities obtained

Diagonalization of conserved quantities achieved

Abstract

We consider the $ su(n) $ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.