Density-matrix-renormalization-group study of excitons in poly-diacetylene chains

TL;DR

This study uses the density-matrix renormalization group method to accurately model excitons in poly-diacetylene chains, reproducing experimental binding energies and revealing dark states and a second exciton.

Contribution

It provides a numerically exact treatment of long-range Coulomb interactions in excitons, improving understanding of their properties in poly-diacetylene chains.

Findings

Reproduces experimental exciton binding energies and polarizability.

Identifies optically dark states below the singlet exciton.

Discovers a weakly bound second exciton with 0.1 eV binding energy.

Abstract

We study the elementary excitations of a model Hamiltonian for the $\pi$-electrons in poly-diacetylene chains. In these materials, the bare band gap is only half the size of the observed single-particle gap and the binding energy of the exciton of 0.5 eV amounts to 20% of the single-particle gap. Therefore, exchange and correlations due to the long-range Coulomb interaction require a numerically exact treatment which we carry out using the density-matrix renormalization group (DMRG) method. Employing both the Hubbard--Ohno potential and the screened potential in one dimension, we reproduce the experimental results for the binding energy of the singlet exciton and its polarizability. Our results indicate that there are optically dark states below the singlet exciton, in agreement with experiment. In addition, we find a weakly bound second exciton with a binding energy of 0.1 eV. The energies in the triplet sector do not match the experimental data quantitatively, probably because we do not include polaronic relaxation effects.