Exponential decay of the critical points in a discrete model of polyacetylene

TL;DR

This paper proves that stationary states in a discrete model of polyacetylene, specifically the SSH model, converge exponentially fast to their asymptotic periodic states, enhancing understanding of their stability and structure.

Contribution

The paper establishes an exponential decay rate for critical points in the SSH model of polyacetylene, providing rigorous mathematical proof of convergence properties.

Findings

Stationary states converge exponentially to asymptotic states

Rigorous proof of exponential decay in the SSH model

Enhanced understanding of polyacetylene's electronic structure

Abstract

In this paper we consider stationary states of the SSH model for infinite polyacetylene chains that are homoclinic or heteroclinic connections between two-periodic dimerized states. We prove that such connections converge exponentially fast to the corresponding asymptotic periodic states.