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Acta Physica Sinica (Overseas Edition)

Ground state and elementary excitations of the Peierls-Hubbard model

Shi Yun-Long, Yumei Zhang, Chen Hong, Xiang Xia Wu

Published Oct 1, 1999• 1 citation
Publisher

Abstract

The ground state and elementary excitations of the Peierls-Hubbard model are studied by using Gaussian wave functional method. The results show that the charge and spin degrees of freedom couple to each other due to the simultaneous existance of the dimerization and Hubbard repulsions. In the region of βs2 > 2π the spin gap ms is still present. Also the influence of Hubbard repulsions on the dimerization is derived from the critical behavior of ground state energy.

DOI
10.1088/1004-423x/8/10/007

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The ground state and elementary excitations of the Peierls-Hubbard model are studied by using Gaussian wave functional method. The results show that the charge and spin degrees of freedom couple to each other due to the simultaneous existance of the dimerization and Hubbard repulsions. In the region of βs2 > 2π the spin gap ms is still present. Also the influence of Hubbard repulsions on the dimerization is derived from the critical behavior of ground state energy.
We investigate critical aspects of the spin-Peierls transition in the one-dimensional half-filled Peierls-Hubbard model. The bosonized Hamiltonian shows that low-energy excitations of the spin and the charge degrees of freedom are coupled through a cross term arising from the transfer-integral alternation. According to the renormalization-group theory, the cross term becomes relevant, which brings about the energy gain and the singlet-triplet gap described by the so-called Cross-Fisher scaling law. To confirm the prediction numerically, the density-matrix renormalization group method is employed. We find that the transition obeys the scaling law; the critical exponents satisfy the hyperscaling relation, whereas a logarithmic correction to the power-law behaviors is suggested. Based on these results, we give a universality argument among the dimerization transition and the criticalities of the two-dimensional qqq-state Potts models (i.e., q=2q=2q=2 and 4) in connection with a role of the on-site Coulomb interaction. Some related experiments on CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ are also discussed.
"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."
We have studied the tendency of the two-dimensional half-filled Hubbard model towards dimerization as a function of the on-site repulsion U. We have found that the phonon with (\ensuremath{\pi},\ensuremath{\pi}) wave vector is the most favorable vibration mode when U is less than a critical value Uc{U}_{c}Uc​, where Uc{U}_{c}Uc​ is a function of the dimerization. When U is greater than Uc{U}_{c}Uc​, the (\ensuremath{\pi},0) phonon becomes preferred. In leading order, the energy gain under dimerization appears to be proportional to ${\ensuremath{\delta}}^{2}$ln\ensuremath{\delta} if the (\ensuremath{\pi},\ensuremath{\pi}) phonon is favorable, so that the system displays a Peierls instability in this case. For large U the energy gain to leading order appears to be proportional to ${\ensuremath{\delta}}^{2}$ for both the (\ensuremath{\pi},\ensuremath{\pi}) and (\ensuremath{\pi},0) phonons, and the latter one is preferred; in that case the system is stable unless the electron-phonon coupling exceeds a critical value. Unlike the effect in the one-dimensional case, the on-site repulsion U seems to have essentially no effect on the tendency towards dimerization for small U, and suppresses it for large U. This difference may be related to the fact that there exists long-range antiferromagnetic order in the two-dimensional half-filled Hubbard model when U is present.
We present detailed studies of the self-interaction-corrected local-spin-density method. As an application, we consider ground-state properties of a highly correlated many-electron system interacting with phonons, namely, the one- and two-dimensional Hubbard-Peierls model. An efficient minimization method is presented which allows one to find fully self-consistent solutions to the self-interaction-corrected local-spin-density total-energy functional without assuming any symmetry of the one-electron states. Charge- and spin-correlation functions, the energy gap, and phonon-induced electronic energy gains for the two-dimensional Hubbard-Peierls model are in significantly better agreement with numerically exact results than the standard local-density method. Noticeably, we find that phonons tend to de- stabilize the antiferromagnetic ground state in two dimensions and show a negative-U behavior in the energy gap, in contrast to the situation in one dimension. This is relevant for the theory of high-temperature superconductivity.
The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.