The Matrix Product Ansatz for integrable U(1)N models in Lunin-Maldacena backgrounds

we obtain through a matrix product ansatz (mpa) the exact solution of the most general n-state spin chain with u(1)n symmetry and nearest neighbour interaction. in the case n = 6 this model contain as a special case the integrable so(6) spin chain related to the one loop mixing matrix for anomalous dimensions in n = 4 sym, dual to type iib string theory in the generalised lunin-maldacena backgrounds. this mpa is construct by a map between scalar fields and abstract operators that satisfy an appropriate associative algebra. we analyses the yang-baxter equation in the n = 3 sector and the consistence of the algebraic relations among the matrices defining the mpa and find a new class of exactly integrable model unknown up to now.