Extracting the Single-Particle Gap in Carbon Nanotubes with Lattice Quantum Monte Carlo

We show how lattice Quantum Monte Carlo simulations can be used to calculate 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 and compare our results to empirical data of the Anti-Ferromagnetic Mott Insulating gap in large diameter tubes.Comment: 8 pages, 5 figures, Lat2017 proceedin

Antiferromagnetic character of the quantum phase transition in the Hubbard model on the honeycomb lattice

We provide a unified, comprehensive treatment of all operators that contribute to the anti-ferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $\beta=0.898(37)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons