Peierls instability for the Holstein model

TL;DR

This paper investigates the Holstein model, demonstrating that in the weak interaction and rational density case, the system's energy landscape features two local minima related to lattice translation symmetry.

Contribution

It provides a rigorous analysis of the energy stationary points in the Holstein model, revealing Peierls instability under specific conditions.

Findings

Energy has two stationary points as local minima

Stationary points are related by lattice translation

Results apply to weak coupling and rational densities

Abstract

We consider the static Holstein model, describing a chain of Fermions interacting with a classical phonon field, when the interaction is weak and the density is a rational number. We show that the energy of the system, as a function of the phonon field, has two stationary points, defined up to a lattice translation, which are local minima in the space of fields periodic with period equal to the inverse of the density.