Quantum Monte Carlo Calculations for Carbon Nanotubes

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.

54 pages, 16 figures, published in Physical Review B

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Cited by in corpus (25)

• Revisiting the Hybrid Quantum Monte Carlo Method for Hubbard and Electron-Phonon Models
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice
• Precise determination of lattice phase shifts and mixing angles
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems
• The Antiferromagnetic Character of the Quantum Phase Transition in the Hubbard Model on the Honeycomb Lattice
• Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• A density of states approach to the hexagonal Hubbard model at finite density
• Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• The Ising Model with Hybrid Monte Carlo
• Quantum Monte Carlo simulation of topological phase transitions
• Sampling General N-Body Interactions with Auxiliary Fields
• Extracting the Single-Particle Gap in Carbon Nanotubes with Lattice Quantum Monte Carlo
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Localization of Electronic States in Hybrid Nano-Ribbons in the Non-Perturbative Regime
• Quantum phase transitions on the hexagonal lattice
• Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration
• Single Particle Spectrum of Doped ${\mathrm{C}}_{20}{\mathrm{H}}_{12}$-Perylene
• Fully ergodic simulations using radial updates
• Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral
• Stochastic and Tensor Network simulations of the Hubbard Model
• Defect engineering spin centers in interacting many-body Su-Schrieffer-Heeger chains