Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models

TL;DR

This paper conjectures hidden Onsager algebra symmetries in two quantum lattice models, linking conserved charges to transfer matrices, and introduces a new construction method for semi-cyclic transfer matrices at roots of unity.

Contribution

It proposes the existence of hidden Onsager algebra symmetries in specific quantum models and develops a novel transfer matrix fusion method for the spin-1 Zamolodchikov-Fateev model.

Findings

Conjectured Onsager symmetries relate to conserved charges.

Constructed semi-cyclic transfer matrices for spin-1 model.

Demonstrated the approach using known models as examples.

Abstract

We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U(1)-invariant clock model. A novel construction of the semi-cyclic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity value of the anisotropy is carried out via transfer matrix fusion procedure.