Integrable inhomogeneous spin chains in generalized Lunin-Maldacena backgrounds

we obtain through a matrix product ansatz the exact solution of the most general inhomogeneous spin chain with nearest neighbor interaction and with u(1)2 and u(1)3 symmetries. these models are related to the one loop mixing matrix of the leigh-strassler deformed n = 4 sym theory, dual to type iib string theory in the generalized lunin-maldacena backgrounds, in the sectors of two and three kinds of fields, respectively. the solutions presented here generalizes the results obtained by the author in a previous work for homogeneous spins chains with u(1)n symmetries in the sectors of n = 2 and n = 3.