Dimerization of polyacetylene using a distance-dependent Hubbard model and the density-matrix renormalization-group method

The dimerization of polyacetylene is studied using a distance-dependent Hubbard Hamiltonian for the valence π electrons and approximating σ-electron contributions by a sum of pair interactions E_σ(rᵢⱼ). The π-electron Coulomb repulsion U is taken to be independent of the C-C distances rᵢⱼ and is varied systematically from the uncorrelated or H\"uckel limit all over to the strongly correlated or Heisenberg regime. For each value of U, E_σ(rᵢⱼ), and the π-electron hopping integral t(rᵢⱼ) are fitted to reproduce ab initio results on the ground-state and first-excited-state energy of the ethylene molecule. The one-dimensional many-body problem is solved numerically by means of the density-matrix renormalization-group (DMRG) method. The ground-state energy E of the infinite open polymer is obtained by extrapolation considering chains of up to 300 atoms. The dimerization δ=(ri,i+1-r_i-1,i)/2 and the average bond length R=(ri,i+1+r_i-1,i)/2 are determined by minimizing E. While R is not significantly affected by the value of U, δ shows a remarkable nonmonotonic behavior. The differences between the delocalized regime, small $U/t$, and spin-Peierls behavior, large $U/t$, are discussed. The convergence properties of the DMRG algorithm are analyzed as a function of U, δ, and the number states kept at each RG step. Criteria are examined in order to control the accuracy of the DMRG calculations in both weakly and strongly correlated situations.