Quantum Monte Carlo Calculations for Carbon Nanotubes

TL;DR

This paper applies lattice Quantum Monte Carlo methods to study the electronic properties of carbon nanotubes, accounting for strong electron-electron interactions, and benchmarks results against simpler models.

Contribution

It introduces a lattice QMC approach for carbon nanotubes with long-range interactions, extending techniques from lattice QCD to nanostructure electronic analysis.

Findings

Successful application to (3,3) nanotube spectrum

Benchmarking against Hubbard models shows accuracy

Method applicable to various nanotubes and nanostructures

Abstract

We show how lattice Quantum Monte Carlo can be applied to the electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. Our lattice Hamiltonian is closely related to the hexagonal Hubbard model augmented by a long-range electron-electron interaction. We apply our method to the single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and consider the effects of strong electron-electron correlations. Our approach is equally applicable to other nanotubes, as well as to other carbon nanostructures. We benchmark our Monte Carlo calculations against the two- and four-site Hubbard models, where a direct numerical solution is feasible.