Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.Comment: 14 pages, 12 figures, tciLaTeX, aip-BibTeX styl

Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory

We show that the scattering interaction between a high energy electron and a photon can be strongly enhanced by different types of localized plasmons in a non-trivial way. The scattering interaction is predicted by an eigen-response theory, numerically verified by finite-difference-time-domain simulation, and experimentally verified by cathodoluminescence spectroscopy. We find that the scattering interaction associated with dark plasmons can be as strong as that of bright plasmons. Such a strong interaction may offer new opportunities to improve single-plasmon detection and high-resolution characterization techniques for high quality plasmonic materials.Comment: 4 pages, 4 figures (excluding Supporting Information

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure

Interaction driven metal-insulator transition in strained graphene

The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between $\pi$-electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that without strain, graphene remains metallic and changing the substrate from SiO$_2$ to suspended samples hardly makes any difference. In contrast, applying a rather large -- but experimentally realistic -- uniform and isotropic strain of about $15\%$ seems to be a promising route to making graphene an antiferromagnetic Mott insulator.Comment: Updated version: 6 pages, 3 figure

The role of electron-electron interactions in two-dimensional Dirac fermions

The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior.Comment: 11 pages, 4 figure

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure