We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (Huckel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the Huckel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zig-zag chains using the density-matrix renormalization group (DMRG) method. We check our numerical approach against analytic results for the Huckel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.
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