| الملخص: | The density matrix renormalization group method is used to investigate the Peierls transition for the extended Hubbard model coupled to quantized phonons. Following our earlier work on spin-Peierls systems, we use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit and a gapless, dispersive (Debye) limit to investigate the entire frequency range. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, and bipartite quantum entanglement. All these probes indicate that a transition of Berezinskii-Kosterlitz-Thouless type is observed at a nonzero electron-phonon coupling gc for a nonvanishing electron-electron interaction. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc for a fixed optical (q=π) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective electron-lattice coupling for the Peierls-active mode. By varying the Coulomb interaction U, we observe a generalized Peierls transition, intermediate between the uncorrelated (U=0) and spin-Peierls (U→) limits, where U is the Hubbard Coulomb parameter. Using the extended Hubbard model with Debye phonons, we investigate the Peierls transition in trans-polyacetylene and show that the transition is close to the critical regime. © 2011 American Physical Society.
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