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arXiv:cond-mat/0210349 · Journal of the Physical Society of Japan

On the Correlation Effect in Peierls–Hubbard Chains

Jiřı́ Málek, Stefan‐Ludwig Drechsler, Sergej Flach A, Eric Jeckelmann, K. Kladko

Published Sep 15, 2003• 7 citations
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Abstract

We reexamine the dimerization, the charge and the spin gaps of a half-filled Peierls-Hubbard chain by means of the incremental expansion technique. Our numerical findings are in significant quantitative conflict with recently obtained results by M. Sugiura and Y. Suzumura [J. Phys. Soc. Jpn. v. 71 (2002) 697] based on a bosonization and a renormalization group method, especially with respect to the charge gap. Their approach seems to be valid only in the weakly correlated case.

DOI
10.1143/jpsj.72.2277

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We reexamine the dimerization, the charge and the spin gaps of a half-filled Peierls-Hubbard chain by means of the incremental expansion technique. Our numerical findings are in significant quantitative conflict with recently obtained results by M. Sugiura and Y. Suzumura [J. Phys. Soc. Jpn. v. 71 (2002) 697] based on a bosonization and a renormalization group method, especially with respect to the charge gap. Their approach seems to be valid only in the weakly correlated case.
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."
The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated by combining an incremental expansion with exact diagonalization of finite chain segments. The ground-state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than 3×10−3 for all values of U using diagonalations of 12-site (20-site) chain segments. For dimerized chains the dimerization order parameter d as a function of the on-site repulsion interaction U has a maximum at nonzero values of U, if the electron-phonon coupling g is lower than a critical value g c . The critical value g c is found with high accuracy to be g c =0.69. For smaller values of g the position of the maximum of d(U) is approximately 3t, and rapidly tends to zero as g approaches g c from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.
Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.
We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitations can be described in terms of an effective antiferromagnetic Heisenberg model. Beyond a critical strength for the nearest-neighbor interaction, the dimerized extended Hubbard model at quarter filling develops a charge-density-wave ground state. The dimerization and the nearest-neighbor Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its value for the bare Hubbard model. We discuss the relevance of our findings for the Bechgaard salts.
We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chains coupled via the interchain one-particle hopping integral t b , by the density-matrix renormalization-group (DMRG) method. Next, we consider the d =1+ε dimensional model, using the perturbative renormalization-group (PRG) method. The dimensionality is controlled through t b and ε, respectively. Both approaches lead to the conclusion that, for a finite dimerization ratio, the charge gap decreases as the dimensionality increases.