The Yangian origin of the Grassmannian integral

In this paper we analyse formulas which reproduce different contributions to scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian integral. Recently their Yangian invariance has been proved directly by using the explicit expression of the Yangian level-one generators. The specific cyclic structure of the form integrated over the Grassmannian enters in a crucial way in demonstrating the symmetry. Here we show that the Yangian symmetry fixes this structure uniquely.Comment: 26 pages. v2: typos corrected, published versio

Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas

The quasiparticle effective mass is a key quantity in the physics of electron gases, describing the renormalization of the electron mass due to electron-electron interactions. Two-dimensional electron gases are of fundamental importance in semiconductor physics, and there have been numerous experimental and theoretical attempts to determine the quasiparticle effective mass in these systems. In this work we report quantum Monte Carlo results for the quasiparticle effective mass of a two-dimensional homogeneous electron gas. Our calculations differ from previous quantum Monte Carlo work in that much smaller statistical error bars have been achieved, allowing for an improved treatment of finite-size effects. In some cases we have also been able to use larger system sizes than previous calculations

Quantum Monte Carlo calculation of the energy band and quasiparticle effective mass of the two-dimensional Fermi fluid

We have used the diffusion quantum Monte Carlo method to calculate the energy band of the two-dimensional homogeneous electron gas (HEG), and hence we have obtained the quasiparticle effective mass and the occupied bandwidth. We find that the effective mass in the paramagnetic HEG increases significantly when the density is lowered, whereas it decreases in the fully ferromagnetic HEG. Our calculations therefore support the conclusions of recent experimental studies [Y.-W. Tan et al., Phys. Rev. Lett. 94, 016405 (2005); M. Padmanabhan et al., Phys. Rev. Lett. 101, 026402 (2008); T. Gokmen et al., Phys. Rev. B 79, 195311 (2009)]. We compare our calculated effective masses with other theoretical results and experimental measurements in the literature

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair correlation function, static structure factor, and momentum density of the ground state of the two-dimensional homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems

Yangian symmetry of light-like Wilson loops

We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.Comment: 15 pages, 5 figure

Electrically Tunable Band Gap in Silicene

We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. We find that the electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electric fields, the interplay between this tunable band gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele spin-orbit coupling induces a transition from a topological to a band insulator, whereas at much higher electric fields silicene becomes a semimetal

Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene

We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA- and AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9) meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations.Comment: 5 pages and 3 figures, submitted to Phys. Rev. Lett.; supplemental material is available on arXiv via the ancillary files attached to this submissio

Electrons and phonons in single layers of hexagonal indium chalcogenides from ab initio calculations

We use density functional theory to calculate the electronic band structures, cohesive energies, phonon dispersions, and optical absorption spectra of two-dimensional In$_2$X$_2$ crystals, where X is S, Se, or Te. We identify two crystalline phases (alpha and beta) of monolayers of hexagonal In$_2$X$_2$, and show that they are characterized by different sets of Raman-active phonon modes. We find that these materials are indirect-band-gap semiconductors with a sombrero-shaped dispersion of holes near the valence-band edge. The latter feature results in a Lifshitz transition (a change in the Fermi-surface topology of hole-doped In$_2$X$_2$) at hole concentrations $n_{\rm S}=6.86\times 10^{13}$ cm$^{-2}$, $n_{\rm Se}=6.20\times 10^{13}$ cm$^{-2}$, and $n_{\rm Te}=2.86\times 10^{13}$ cm$^{-2}$ for X=S, Se, and Te, respectively, for alpha-In$_2$X$_2$ and $n_{\rm S}=8.32\times 10^{13}$ cm$^{-2}$, $n_{\rm Se}=6.00\times 10^{13}$ cm$^{-2}$, and $n_{\rm Te}=8.14\times 10^{13}$ cm$^{-2}$ for beta-In$_2$X$_2$.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1302.606

On the Classification of Residues of the Grassmannian

We study leading singularities of scattering amplitudes which are obtained as residues of an integral over a Grassmannian manifold. We recursively do the transformation from twistors to momentum twistors and obtain an iterative formula for Yangian invariants that involves a succession of dualized twistor variables. This turns out to be useful in addressing the problem of classifying the residues of the Grassmannian. The iterative formula leads naturally to new coordinates on the Grassmannian in terms of which both composite and non-composite residues appear on an equal footing. We write down residue theorems in these new variables and classify the independent residues for some simple examples. These variables also explicitly exhibit the distinct solutions one expects to find for a given set of vanishing minors from Schubert calculus.Comment: 20 page