The Landau-Peierls distortion in the linear acetylenic carbon chain: an ab-initio study of the interplay between electronic correlations and anharmonic lattice dynamics

The linear acetylenic carbon chain (or carbyne) is the simplest example of a 1D carbon system and the prototype of a charge-density wave (CDW). As a matter of fact, at the harmonic level, it undergoes a Landau-Peierls phase transition from an orderered metallic phase (cumulene) to a distorted insulating phase (polyyne) due to an unstable phonon mode with momentum 2k_F (where k_F is the Fermi momentum). Its existence is still controversial: while both the Coleman and the Mermin-Wagner-Hohenberg theorems prevent polyyne from existing at any temperature, Landau and Peierls showed that the long-range nature of interatomic forces stabilizes the distorted system.

In this work we re-investigate the Landau-Peierls distortion of carbyne from first principles, departing from the harmonic description of lattice dynamics and taking into account electronic correlations. Moreover, thanks to the stochastic self-consistent harmonic approximation (SSCHA), we also study the temperature dependent free energy landscape by including phonon-phonon anharmonic interactions in a non-perturbative way.