The Quantum Algebraic Structure of the Twisted XXZ Chain

TL;DR

This paper explores the algebraic structure of a twisted XXZ spin chain using a two-parameter quantum algebra, providing insights into its integrability and boundary conditions.

Contribution

It introduces a new R-matrix depending on two parameters and identifies the underlying algebra as a two-parameter deformed algebra $SU_{q,t}(2)$ with a central element.

Findings

Identified the algebraic structure as $SU_{q,t}(2)$ with a central element.

Derived the Hamiltonian for the twisted XXZ model with new boundary conditions.

Connected the algebraic framework to the integrability of the spin chain.

Abstract

We consider the Quantum Inverse Scattering Method with a new R-matrix depending on two parameters $q$ and $t$. We find that the underlying algebraic structure is the two-parameter deformed algebra $SU_{q,t}(2)$ enlarged by introducing an element belonging to the centre. The corresponding Hamiltonian describes the spin-1/2 XXZ model with twisted periodic boundary conditions.