The Role of the Central Element in the Quantum Algebra Underlying the Twisted XXZ Chain

TL;DR

This paper investigates the algebraic structure of the twisted XXZ Heisenberg model, focusing on the central element's role and its connection to twisted boundary conditions, enhancing understanding of integrable quantum systems.

Contribution

It reveals the significance of a non-trivial central element in the algebra and its influence on the boundary conditions of the twisted XXZ chain.

Findings

Identification of the central element's role in the algebraic structure.

Connection between the central element and twisted boundary conditions.

Insights into the algebraic underpinnings of the twisted XXZ model.

Abstract

We study the relationship among the XXZ Heisenberg model and three models obtained from it by various transformations. In particular, we emphasize the role of a non trivial central element $t^Z$ in the underlying algebra and its relationship with the twisted boundary conditions, $S^{\pm}_{N+1}=t^{\pm N}S^{\pm}_1$.