2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55575The finite XXZ spin chain with boundaries is studied. We derive the transfer matrix from the q-difference equation discovered by Cherednik and construct its eigenstates by the vertex operator approach. We point out that the eigenstates with no magnetic fields have a symmetry called the turning symmetry. Making use of this symmetry we calculate the spontaneous magnetization in the thermodynamic limit, which is roughly twice as large as that in the half-infinite XXZ spin chain.19pages, LaTeX2e file, minor correctionsHigh Energy Physics - TheoryCondensed MatterQuantum AlgebraExactly Solvable and Integrable Systemstext