Quantum Galilei Group as Symmetry of Magnons

TL;DR

This paper introduces the quantum Galilei group as a symmetry of magnons in the 1D Heisenberg ferromagnet, demonstrating how inhomogeneous quantum groups can effectively describe integrable systems and their solutions.

Contribution

It presents the quantum Galilei group Gamma_q(1) as a new symmetry algebra for magnons, providing a novel algebraic framework for analyzing integrable quantum systems.

Findings

Quantum Galilei group Gamma_q(1) describes magnon symmetries.

Complete algebraic description of single magnon and bound states.

Inhomogeneous quantum groups relate to Bethe ansatz solutions.

Abstract

Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems and to provide solutions equivalent to the Bethe ansatz. The method is illustrated on the 1D Heisenberg ferromagnet whose symmetry is shown to be the quantum Galilei group Gamma_q(1) here introduced. Both the single magnon and the s=1/2 bound states of n-magnons are completely described by the algebra.