Charge-density-wave instability in the Holstein model with quartic anharmonic phonons

TL;DR

This paper investigates how quartic anharmonic phonons influence charge-density-wave instabilities in a one-dimensional electron system, providing an exact theoretical framework for understanding these effects in molecular-crystal models.

Contribution

It derives an exact expression for the phonon-mediated two-electron action in a model with quartic anharmonic phonons and analyzes their impact on charge-density-wave transition temperatures.

Findings

Quartic anharmonic phonons significantly affect CDW transition temperatures.

Non-perturbative approach yields exact two-electron action.

Charge-density-wave instability is sensitive to anharmonic phonon effects.

Abstract

The molecular-crystal model, that describes a one-dimensional electron gas interacting with quartic anharmonic lattice vibrations, offers great potentials in the mapping of a relatively wide range of low-dimensional fermion systems coupled to optical phonons onto quantum liquids with retarded interactions. Following a non-perturbative approach involving non-Gaussian partial functional integrations of lattice degrees of freedom, the exact expression of the phonon-mediated two-electron action for this model is derived. With the help of Hubbard-Stratonovich transformation the charge-density-wave instability is examined in the sequel, with particular emphasis on the effect of the quartic anharmonic phonons on the charge-density-wave transition temperature.