Generalization of the matrix product ansatz for integrable chains

We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present on our previous articles ( F. C. Alcaraz and M. J. Lazo J. Phys. A: Math. Gen. 37 (2004) L1-L7 and J. Phys. A: Math. Gen. 37 (2004) 4149-4182.) In [1] (to which we refer hereafter as I) and [2], we formulate a matrix product ansatz (MPA) for a large family of exactly integrable spin chains such as the anisotropic Heisenberg model, Fattev-Zamolodchikov model, IzerginKorepin model, Sutherland model, t-J model, Hubbard model, etc. In this note we present a generalization of the MPA for periodic quantum chains. The generalization is important since it allows, at least in some cases, finitedimension representations of the matrices defining the MPA. In order to illustrate this generalization we consider the standard XXZ quantum chain with periodic boundary condition, H = − 1 2 L