Quasi-local conserved charges and spin transport in spin-$1$ integrable chains

Understand

We consider the integrable one-dimensional spin-$1$ chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian.

• The latter is parametrized, analogously to the XXZ spin-$1/2$ model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-$1$ Babujian-Takhtajan Hamiltonian.
• Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-$1$ ZF chain.
• Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded.