Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry

TL;DR

This paper explores the spinon excitations in the integrable spin-1 FZ chain, revealing their connection to hidden supersymmetry and constructing supersymmetric eigenstates, bridging lattice models and field theory.

Contribution

It uncovers the action of supercharges on the FZ chain's degrees of freedom and constructs supersymmetric eigenstates, linking lattice models with supersymmetric field theories.

Findings

Supercharges act nontrivially on FZ chain degrees of freedom.

Eigenstates invariant under supersymmetric Hamiltonian are constructed.

Supercharges' actions match those in the supersymmetric sine-Gordon model.

Abstract

We study spinon excitations of the integrable spin-1 (Fateev-Zamolodchikov; FZ) chain and their relation to the hidden supersymmetry. Using the notion of the supercharges earlier introduced to the spin chains, which change the system length by one, we found that they nontrivially act on one of two kinds of the degrees of freedom for the FZ chain. Their actions were obtained to be the same as those of the supercharges defined on the supersymmetric sine-Gordon model, the low-energy effective field theory of the FZ chain. Moreover, we construct the eigenstates which are invariant under the supersymmetric Hamiltonian given as the anti-commutator of the supercharges.