The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis, exploiting the charge and spin conservation as well as the electron-hole and spin-parity symmetries. We employ the $U-V-δ$ Hamiltonian which is a simplified version of the PPP Hamiltonian. For several coupling constants $U$ and $V$ and dimerizations $δ$ we compute the GS energy per monomer which agrees within a $2%-4%$ accuracy with the DMRG results. We also show the evolution of the MP-variational parameters in the weak and strong dimerization regimes.

18 pages, 2 figs and 3 tables. RevTex