Correlation Effect on the Two-Dimensional Peierls Phase

TL;DR

This paper investigates how electron-electron interactions influence Peierls lattice distortions in a two-dimensional model, revealing that fluctuations significantly modify the multimode bond order wave properties and phase transition behaviors.

Contribution

It introduces a second-order perturbation approach to analyze fluctuation effects on Peierls distortions, extending previous Hartree-Fock results and highlighting the impact on multimode BOW Fourier components.

Findings

Fourier components of BOW increase with electron-electron interaction strength.

Fluctuation effects strongly affect the wave vector component related to the smallest reciprocal lattice vector.

Phase transition between BOW and SDW remains first order despite fluctuations.

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 $\mathbf{Q}$ 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 $\mathbf{Q}$ 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.