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Journal of Jimei University Natural Science

Peierls Transition in One Dimensional Strongly Correlated Electron System

Lin Qiu-Bao

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

An one-dimensional large-U Hubbard-Peierls Hamiltonian is proposed to discuss the Peierls transition in the strongly correlated electron system.It is shown that this system can cause a dimerization transition induced by the anti-ferromagnetic spin-wave and the phonon interaction.And the transition temperature T d shows decrease when the doping parameter increases.The treatment is valid at region of δt≥J.

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Physical review. B, Condensed matter•Mar 29, 2002•6 citations
An one-dimensional large-U Hubbard-Peierls Hamiltonian is proposed to discuss the Peierls transition in the strongly correlated electron system.It is shown that this system can cause a dimerization transition induced by the anti-ferromagnetic spin-wave and the phonon interaction.And the transition temperature T d shows decrease when the doping parameter increases.The treatment is valid at region of δt≥J.
We demonstrate that a Peierls dimerization can occur in ferromagnetic spin chains activated by thermal fluctuations. The dimer order parameter and entanglement measures are studied as functions of the modulation of the magnetic exchange interaction and temperature, using a spin-wave theory and the density-matrix renormalization group. We discuss the case where a periodic modulation is caused by spin-phonon coupling and the case where electronic states effectively induce such a modulation. The importance of the latter for a number of transition metal oxides is highlighted.
We study extended Hubbard and Peierls-Hubbard models with up to N=10 sites and half-filled bands with modified boundary conditions. For the extended Hubbard model, the finite-size dependence of the transition from the charge-density-wave regime (CDW) to the spin-density-wave (SDW) regime and of the condensation transition is critically examined, clarifying some previous results. For the Peierls-Hubbard model and N\ensuremath{\le}10 with modified periodic boundary conditions, we always see a decrease of dimerization with U. Extrapolating these results to infinite N, we find that dimerization is enhanced by U for small electron-phonon coupling \ensuremath{\alpha}\ifmmode \tilde{}\else \~{}\fi{}0.75, whereas it decreases with U for 0.75\ensuremath{\le}1. By extending this model by a nearest-neighbor repulsion V, the amplitude of dimerization reaches a maximum at the same value U\ensuremath{\le}2V, where the CDW-to-SDW transition occurs in the extended Hubbard model.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1
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.
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.