Excitons in the One-Dimensional Hubbard Model: a Real-Time Study

TL;DR

This paper investigates the real-time behavior of holon-doublon pairs in a one-dimensional Hubbard insulator, revealing their long-lived nature, bound states, and propagation characteristics, with implications for solar cell technology.

Contribution

It provides new insights into holon-doublon dynamics in 1D Hubbard models, highlighting long-lived pairs and bound states due to Coulomb interactions.

Findings

Holon-doublon pairs are long-lived with inefficient decay to spin excitations.

Part of the wave-function remains bound when inter-site Coulomb repulsion is present.

Holon and doublon move in opposite directions in 1D without external fields.

Abstract

We study the real-time dynamics of a pair hole/doubly-occupied-site, namely a holon and a doublon, in a 1D Hubbard insulator with on-site and nearest-neighbor Coulomb repulsion. Our analysis shows that the pair is long-lived and the expected decay mechanism to underlying spin excitations is actually inefficient. For a nonzero inter-site Coulomb repulsion, we observe that part of the wave-function remains in a bound state. Our study also provides insight on the holon-doublon propagation in real space. Due to the one-dimensional nature of the problem, these particles move in opposite directions even in the absence of an applied electric field. The potential relevance of our results to solar cell applications is discussed.