5 problems

Let $\mathbf{Z}_{n}$ and $\mathbf{Y}_{n}$ be the higher-order Z and Y charges, let $\mathbf{Q}^{0}_{m}$ and $\mathbf{Q}^{-}_{m}$ be the corresponding higher-order Onsager generator…

Consider a highest weight representation of the $sl_2$ loop algebra arising in the setting of the six-vertex model at roots of unity, and the Onsager algebra symmetry of the chiral…

Integrability conjecture. The Hamiltonian $\mathsf{H}^{\rm FM}(r,\theta)$ is integrable for arbitrary $r\in\mathbb{Z}_{>0}$ and $0\leq\theta<2\pi$. This proposes an integrable inte…

Let the spin-$1/2$ XXZ model be evaluated at a root-of-unity anisotropy, and let the Onsager algebra be regarded as a subalgebra of the $\mathfrak{sl}_{2}$ loop algebra. Onsager sy…

Let the spin-$1/2$ XXZ model and the spin-1 ZF model be evaluated at root-of-unity values of the anisotropy. A Hamiltonian is $U(1)$-invariant when it commutes with both Onsager ge…