Staggered Anisotropy Parameter Modification of the Anisotropic $t-J$ Model

The anisotropic t-J model ($U_q(gl(2\mathrm{\mid }1))$ Perk-Schultz model) with staggered disposition of the anisotropy parameter along a chain is considered and the corresponding ladder type integrable model is constructed. This is a generalisation to spin-1 case of the staggered $XXZ$ spin-1/2 model considered earlier. The corresponding Hamiltonian is calculated and, since it contains next to nearest neighbour interaction terms, can be written in a zig-zag form. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found.