On integrable Hamiltonians for higher spin XXZ chain

TL;DR

This paper constructs and analyzes integrable Hamiltonians for higher spin XXZ chains, providing explicit examples and exploring their algebraic properties and symmetries, including modifications leading to open chain integrability.

Contribution

It introduces explicit higher spin Hamiltonians for the XXZ chain and studies their relations and symmetries, including a novel modification for open chains.

Findings

Explicit higher spin Hamiltonians up to spin 3/2

Relations between U_q(sl_2) and U(1) symmetric r-matrices

A modified Hamiltonian for open chains with integrability

Abstract

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U_q(sl_2)-symmetric Hamiltonian for an open chain.