# Incommensurate quantum-size oscillations in acene-based molecular wires - effects of quantum fluctuations

## TL;DR

This paper investigates the quantum-size oscillations in acene-based molecular wires, demonstrating that these oscillations persist despite electron interactions, using a combination of theoretical models and numerical methods.

## Contribution

It provides a detailed analysis showing that incommensurate gap oscillations remain robust in acene ladders even when electron-electron interactions are considered.

## Key findings

- Incommensurate gap oscillations persist for a range of interaction strengths.
- Interactions can potentially open a large gap, but do not eliminate oscillations.
- The study combines Hartree-Fock and DMRG methods for analysis.

## Abstract

Molecular wires of the acene-family can be viewed as a physical realization of a two-rung ladder Hamiltonian. For acene-ladders, closed-shell ab-initio calculations and elementary zone-folding arguments predict incommensurate gap oscillations as a function of the number of repetitive ring units, $N_{\text{R}}$, exhibiting a period of about ten rings. %% Results employing open-shell calculations and a mean-field treatment of interactions suggest anti-ferromagnetic correlations that could potentially open a large gap and wash out the gap oscillations. % Within the framework of a Hubbard model with repulsive on-site interaction, $U$, we employ a Hartree-Fock analysis and the density matrix renormalization group to investigate the interplay of gap oscillations and interactions. % We confirm the persistence of incommensurate oscillations in acene-type ladder systems for a significant fraction of parameter space spanned by $U$ and $N_{\text{R}}$.