Abstract
The dimerization of polyacetylene is studied in the framework of a distance dependent Hubbard Hamiltonian for the valence π electrons. The underlying one-dimensional many-body problem is solved numerically using the density matrix renormalization group (DMRG) method and the resulting ground-state energy is optimized in order to determine the dimerization δ and the average bond-length EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOuayaara % aaaa!36E3!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ \bar R $$. The strength of the Coulomb repulsion U/t is varied from the uncorrelated or Hückel limit all over to the strongly correlated or Heisenberg case. While EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOuayaara % aaaa!36E3!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ \bar R $$ is not significantly affected by the value of U/t, δ shows a remarkable non-monotonic behavior. The differences between the bond-order-wave (small U/t) and the spin-Peierls (large U/t) regimes are discussed.
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For finite U minor differences result from the fact that we fit t(r ij ) by using the Hubbard Hamiltonian.
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Pastor, G.M., Lepetit, M.B. (1998). Bond-Order-Wave versus Spin-Density-Wave Dimerization in Polyacetylene. In: Morán-López, J.L. (eds) Current Problems in Condensed Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9924-8_5
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DOI: https://doi.org/10.1007/978-1-4757-9924-8_5
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