Phase transition in the Peierls model for polyacetylene

TL;DR

This paper analyzes the Peierls model for polyacetylene chains, demonstrating a temperature-dependent phase transition from insulating to metallic behavior, with a critical temperature that diminishes exponentially with chain rigidity.

Contribution

It proves the existence of a critical temperature for dimerization in the Peierls model and characterizes its dependence on chain rigidity, extending understanding of phase transitions in conjugated polymers.

Findings

Existence of a critical temperature for dimerization

Chain is insulating below and metallic above the critical temperature

Critical temperature is exponentially small in chain rigidity

Abstract

We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical temperature below which the chain is dimerized, and above which it is 1-periodic. The chain behaves like an insulator below the critical temperature and like a metal above it. We characterize the critical temperature in the thermodynamic limit model, and prove that it is exponentially small in the rigidity of the chain. We study the phase transition around this critical temperature.