Solitonic approach to the dimerization problem in correlated one-dimensional systems

Using exact diagonalizations, we consider self-consistently the lattice distortions in odd Peierls-Hubbard and spin-Peierls periodic rings in the adiabatic harmonic approximation. From the tails of the inherent spin soliton the dimerization d(infinity) of regular even rings is found by extrapolations to infinite ring lengths. Considering a wide region of electron-electron on-site interaction values U>0 compared with the band width 4t(0) at intermediately strong electron-phonon interaction g, known relationships obtained by other methods are reproduced and/or refined within one unified approach: an example is the maximum of d(infinity) at U similar or equal to 3t(0) for g similar or equal to 0.5 and its shift to zero for g-->g(c) approximate to 0.7. The hyperbolic tangent shape of the spin soliton is retained for any U and g less than or similar to 0.6. In the spin-Peierls limit the d(infinity) are found to be in agreement with results of density-matrix-renormalizalion-group computations.