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arXiv:cond-mat/0509634 · AIP conference proceedings

Correlation Effect on the Two-Dimensional Peierls Phase

Shutaro Chiba, Yoshiyuki Ono

Published Jan 1, 2006• 6 citations
arXivHTMLPDF

Abstract

The effect of the electron‐electron (e‐e) interaction on the Peierls lattice distortions due to the electron‐lattice (e‐l) interaction is studied in the two‐dimensional Peierls‐Hubbard model, treating the fluctuation of e‐e interaction around the Hartree‐Fock solution within the 2nd order perturbation theory. In our previous work, using the Hartree‐Fock approximation, we found multimode Peierls lattice distortions with wave vectors, the nesting vector Q and those parallel to it, are not affected by an e‐e interaction if it is weak compared with the e‐l coupling. The phase transition between the BOW (bond order wave) with multimode lattice distortions and the SDW (spin density wave) with the wave vector Q behaves as the 1st order transition. The property of the multimode BOW is found to change drastically when we consider the fluctuation effect within the 2nd order perturbation theory. The Fourier components of the multimode BOW increase gradually as the e‐e interaction parameter is increased. Especially the Fourier component with the wave vector equal to the smallest reciprocal lattice vector in the presence of the multimode BOW is most strongly affected by the fluctuation effect.

DOI
10.1063/1.2355195

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Physical review. B, Condensed matter•Nov 15, 1996•8 citations
The effect of the electron‐electron (e‐e) interaction on the Peierls lattice distortions due to the electron‐lattice (e‐l) interaction is studied in the two‐dimensional Peierls‐Hubbard model, treating the fluctuation of e‐e interaction around the Hartree‐Fock solution within the 2nd order perturbation theory. In our previous work, using the Hartree‐Fock approximation, we found multimode Peierls lattice distortions with wave vectors, the nesting vector Q and those parallel to it, are not affected by an e‐e interaction if it is weak compared with the e‐l coupling. The phase transition between the BOW (bond order wave) with multimode lattice distortions and the SDW (spin density wave) with the wave vector Q behaves as the 1st order transition. The property of the multimode BOW is found to change drastically when we consider the fluctuation effect within the 2nd order perturbation theory. The Fourier components of the multimode BOW increase gradually as the e‐e interaction parameter is increased. Especially the Fourier component with the wave vector equal to the smallest reciprocal lattice vector in the presence of the multimode BOW is most strongly affected by the fluctuation effect.
The effects of electron–electron (e–e) interactions on the two-dimensional (2D) Peierls state are discussed using the 2D Peierls–Hubbard model (2D PHM) in the limit of U ≫ t 0 , where U is the on-site e–e interaction parameter between up and down spin electrons and t 0 is the electron transfer integral between nearest neighbor sites. In this limit, the 2D PHM can be mapped onto the 2D spin-Peierls model (2D SPM) in which the effect of the lattice distortion is taken into account in the spin exchange interaction of the 2D Heisenberg model. As was demonstrated in a previous paper [J. Phys. Soc. Jpn. 69 (2000) 1769], the ground state of the 2D electron–lattice (e–l) system (the 2D 1/2-filled SSH model) is the so-called multimode Peierls state where the lattice distortion involves Fourier components with the nesting wave vector Q =(π/ a ,π/ a ), a being the lattice constant, and with those paralell to it. Using the exact diagonalization technique it is shown that the spin-Peierls transition with a mutlimode lattice distortion can occur in the 2D spin–lattice system similarly as in the 2D e–l system.
The two-dimensional Peierls-Hubbard model is studied at half filling within both Hartree-Fock and Kotliar-Ruckenstein slave-boson theory. The interplay between two types of long-range order, bond-order wave (BOW) and antiferromagnetism (AFM), is analyzed for two representative dimerization patterns, corresponding both to the same wave vector $(\ensuremath{\pi},\ensuremath{\pi}).$ For each pattern, the Peierls dimerization (and associated BOW) is weakened and finally suppressed with increasing Hubbard on-site interaction, and correspondingly AFM is gradually enhanced. In particular, a coexistence regime with both BOW and AFM order is established in the parameter space of electron-lattice and Hubbard interactions.
The effect of quantum lattice fluctuations is investigated in a half-filled one-dimensional Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated by introducing the polaronic transformation and the squeezed-phonon state. The electronic correlations are treated by means of a modified Gutzwiller approach and a unified description for the long-range charge-density-wave (CDW) ordering state and the short-range antiferromagnetic correlated state has been developed. The main result is a rather good description of the continuous variation of the dimerization as functions of the Hubbard U and \ensuremath{\omega} is given, which is in good agreement with that of the numerical simulations. The results of the squeezed-polaron theory are shown to be better than those of the ordinary polaron theory. A continuous phase transition is found between the long-range CDW ordering state and the short-range antiferromagnetic correlated state with a transition point different from the prediction of the Hartree-Fock decoupling. The effect of quantum lattice fluctuations on the transition point is also discussed.
The authors study a one-dimensional extended Hubbard-Peierls model in the infinite intracell Coulomb repulsion limit, which is equivalent to a system of spinless electrons. They consider first- and second-neighbor Coulomb repulsion, and two types of phonon are coupled to the electronic system: intramolecular and longitudinal, intercell vibrations. The special case of half an electron per cell is considered. The model is solved in the Hartree-Fock approximation by assuming a possible symmetry break of period two. The solution is obtained for all temperatures. They construct a phase diagram with respect to temperature and the system parameters. Three types of low temperature ordered phase appear: bond ordered waves (BOW), charge ordered waves (COW) and an intermediate phase, across which the transition BOW to COW is continuous. This phase corresponds to a ferroelectric state (F). As temperature is increased from zero, the system undergoes different phase transitions, following a particular sequence, according to its characteristic parameters. At high temperatures the system stabilises in a homogeneous (disordered) phase (H). For some parameters the sequence BOW to F to COW to H is possible. The last result is very striking, since it implies that, on increasing temperature, the symmetry of the system can decrease, as is the case for the BOW to F transition, where the inversion symmetry is lost. This special BOW to F phase transition also occurs in the non-interacting limit, where the results are exact.
The effect of an on-site electron-phonon (e-ph) interaction is studied within the framework of an extended Hubbard model in one dimension. We have eliminated the local phonon coordinates using a modified Lang-Firsov transformation and diagonalized the effective electronic Hamiltonian by a real space renormalization group technique to determine the transition from a charge density wave (CDW) state to a spin density wave (SDW) state. It turns out that the CDW phase is favored by the e-ph coupling with an appreciable band-narrowing effect. In the SDW phase the distortions produced at nearest neighbor sites due to the e-ph interaction become comparable to the on-site distortions while this retardation effect is negligible in the CDW phase. \textcopyright{} 1996 The American Physical Society.