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

TL;DR

This paper employs a solitonic approach with exact diagonalizations to analyze lattice distortions and dimerization in correlated one-dimensional systems, refining known relationships and aligning with DMRG results.

Contribution

It introduces a unified solitonic method to study dimerization in correlated 1D systems, extending previous results and providing detailed insights across various interaction strengths.

Findings

Dimerization d_∞ peaks at U ≈ 3 t_0 for g ≈ 0.5

Dimerization vanishes as g approaches g_c ≈ 0.7

Results agree with DMRG computations in the spin-Peierls limit

Abstract

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_\infty of regular even rings is found by extrapolations to infinite ring lengths. Considering a wide region of electron-electron onsite 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: such as the maximum of d_\infty at U \simeq 3 t_0 for g \simeq 0.5 and its shift to zero for g \to g_c \approx 0.7. The hyperbolic tangent shape of the spin soliton is retained for any U and g <~ 0.6. In the spin-Peierls limit the d_\infty are found to be in agreement with results of DMRG computations.