We consider a simplified model of Polyacetylene introduced by Su, Schrieffer and Cheeger in 1979, which belongs to the class of Peierls models at half-filling. In 1987 Kennedy and Lieb studied finite chains and proved that if the number $N$ of nuclei is even, the energy has exactly two minimisers which are periodic of period $2$, and are translates of one another by a translation of one unit in the lattice. We study rigorously the case of an odd number of atoms. We prove that if $N$ is odd and converges to infinity, the global minimizer of the energy converges to a "kink" soliton in the infinite chain. This soliton is asymptotic to one of the periodic minimizers found by Kennedy-Lieb in one direction of the chain, and to the other solution in the other direction.
This is joint work with Mauricio Garcia Arroyo.