Exactly conserved quasilocal operators for the XXZ spin chain

We extend T Prosen's construction of quasilocal conserved quantities for the XXZ model (2011 Phys. Rev. Lett. 106 217206) to the case of periodic boundary conditions. These quasilocal operators stem from a two-parameter transfer matrix which employs a highest-weight representation of the quantum group algebra inherent in the Yang-Baxter algebra. In contrast with the open chain, where the conservation law is weakly violated by boundary terms, the quasilocal operators in the periodic chain exactly commute with the Hamiltonian and other local conserved quantities.