Conjectures on hidden Onsager algebra symmetries in interacting quantum lattice models
Yuan Miao
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 values of the anisotropy is carried out via the transfer matrix fusion procedure.
Topics & Concepts
Root of unityHomogeneous spaceTransfer matrixLattice (music)Integrable systemQuantumConjectureTransfer (computing)PhysicsMathematicsAnisotropyFusion rulesObservableMathematical physicsQuantum mechanicsRoot (linguistics)Lattice model (finance)Pure mathematicsMatrix (chemical analysis)Theoretical physicsAlgebra over a fieldMatrix algebraChiral modelPrimitive root modulo nCurrent algebraCharge (physics)Conserved quantityQuantum algebraLattice problemQuantum field theoryAlgebraic structures and combinatorial modelsQuantum many-body systemsQuantum Mechanics and Non-Hermitian Physics