Spin-Anisotropy Commensurable Chains: Quantum Group Symmetries and N=2 SUSY

TL;DR

This paper explores integrable 2D quantum spin chains with quantum group symmetries at roots of unity, revealing distinct behaviors based on N-parity and uncovering new integrable deformations and physical properties.

Contribution

It introduces a novel class of higher spin XXZ chains with commensurability conditions linked to quantum groups at roots of unity, analyzing their integrability and physical characteristics.

Findings

N even case exhibits supersymmetric S-matrices

N odd case lacks supersymmetry and bootstrap validity

Magnetization behavior depends on magnetic field sign

Abstract

In this paper we consider a class of the 2D integrable models. These models are higher spin XXZ chains with an extra condition of the commensurability between spin and anisotropy. The mathematics underlying this commensurability is provided by the quantum groups with deformation parameter being an Nth root of unity. Our discussion covers a range of topics including new integrable deformations, thermodynamics, conformal behaviour, S-matrices and magnetization. The emerging picture strongly depends on the N-parity. For the N even case at the commensurable point, S-matrices factorize into N=2 supersymmetric Sine-Gordon matrix and an RSOS piece. The physics of the N odd case is rather different. Here, the supersymmetry does not manifest itself and the bootstrap hypothesis fails. Away from the commensurable point, we find an unusual behaviour. The magnetization of our chains depends on the sign of the external magnetic field.