Exactly conserved quasilocal operators for the XXZ spin chain

TL;DR

This paper generalizes the construction of quasilocal conserved operators for the XXZ spin chain to periodic boundary conditions, ensuring exact commutation with the Hamiltonian and local conserved quantities.

Contribution

It introduces a two-parameter transfer matrix approach using quantum group representations for the periodic XXZ model, extending previous open chain results.

Findings

Quasilocal operators exactly commute with the Hamiltonian in the periodic chain.

Extension of conservation laws from open to periodic boundary conditions.

Use of a two-parameter transfer matrix based on quantum group algebra.

Abstract

We extend T. Prosen's construction of quasilocal conserved quantities for the XXZ model [Phys. Rev. Lett. 106, 217206 (2011)] 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.