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arXiv:cond-mat/9708234 · Physical review. B, Condensed matter

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

Jiřı́ Málek, Stefan‐Ludwig Drechsler, Gernot Paasch, K. Hallberg

Published Oct 1, 1997• 13 citations
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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 ${d}_{\ensuremath{\infty}}$ 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 ${d}_{\ensuremath{\infty}}$ at $U\ensuremath{\simeq}{3t}_{0}$ for $g\ensuremath{\simeq}0.5$ and its shift to zero for $g\ensuremath{\rightarrow}{g}_{c}\ensuremath{\approx}0.7.$ The hyperbolic tangent shape of the spin soliton is retained for any $U$ and $g\ensuremath{\lesssim}0.6.$ In the spin-Peierls limit the ${d}_{\ensuremath{\infty}}$ are found to be in agreement with results of density-matrix-renormalization-group computations.

DOI
10.1103/physrevb.56.r8467

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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\ensuremath∞{d}_{\ensuremath{\infty}}d\ensuremath∞​ of regular even rings is found by extrapolations to infinite ring lengths. Considering a wide region of electron-electron on-site interaction values U>0U>0U>0 compared with the band width 4t0{4t}_{0}4t0​ at intermediately strong electron-phonon interaction g,g,g, known relationships obtained by other methods are reproduced and/or refined within one unified approach: an example is the maximum of d\ensuremath∞{d}_{\ensuremath{\infty}}d\ensuremath∞​ at U\ensuremath≃3t0U\ensuremath{\simeq}{3t}_{0}U\ensuremath≃3t0​ for g\ensuremath≃0.5g\ensuremath{\simeq}0.5g\ensuremath≃0.5 and its shift to zero for g\ensuremath→gc\ensuremath≈0.7.g\ensuremath{\rightarrow}{g}_{c}\ensuremath{\approx}0.7.g\ensuremath→gc​\ensuremath≈0.7. The hyperbolic tangent shape of the spin soliton is retained for any UUU and g\ensuremath≲0.6.g\ensuremath{\lesssim}0.6.g\ensuremath≲0.6. In the spin-Peierls limit the d\ensuremath∞{d}_{\ensuremath{\infty}}d\ensuremath∞​ are found to be in agreement with results of density-matrix-renormalization-group computations.
We study extended Hubbard and Peierls-Hubbard models with up to N=10 sites and half-filled bands with modified boundary conditions. For the extended Hubbard model, the finite-size dependence of the transition from the charge-density-wave regime (CDW) to the spin-density-wave (SDW) regime and of the condensation transition is critically examined, clarifying some previous results. For the Peierls-Hubbard model and N\ensuremath{\le}10 with modified periodic boundary conditions, we always see a decrease of dimerization with U. Extrapolating these results to infinite N, we find that dimerization is enhanced by U for small electron-phonon coupling \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}0.75, whereas it decreases with U for 0.75\ensuremath{\le}1. By extending this model by a nearest-neighbor repulsion V, the amplitude of dimerization reaches a maximum at the same value U\ensuremath{\le}2V, where the CDW-to-SDW transition occurs in the extended Hubbard model.
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