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Conformational isomers or conformers of molecules play a decisive role in chemistry and biology. However, experimental methods to investigate chemical reaction dynamics are typically not conformer-sensitive. Here, we report on a gas-phase megaelectronvolt ultrafast electron diffraction investigation of {\alpha}-phellandrene undergoing an electrocyclic ring-opening reaction. We directly image the evolution of a specific set of {\alpha}-phellandrene conformers into the product isomer predicted by the Woodward-Hoffmann rules in real space and time. Our experimental results are in quantitative agreement with nonadiabatic quantum molecular dynamics simulations, which provide unprecedented detail of how conformation influences time scale and quantum efficiency of photoinduced ring-opening reactions. Due to the prevalence of large numbers of conformers in organic chemistry, our findings impact our general understanding of reaction dynamics in chemistry and biology.

Investigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang-Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin-correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.

X-ray absorption spectroscopy (XAS) is a powerful and well established technique with sensitivity to elemental and chemical composition. Despite these advantages, its implementation has not kept pace with the development of ultrafast pulsed x-ray sources where XAS can capture femtosecond chemical processes. X-ray Free Electron Lasers (XFELs) deliver femtosecond, narrow bandwidth ($\frac{\Delta E}{E} < 0.5\%$) pulses containing $\sim 10^{10}$ photons. However, the energy contained in each pulse fluctuates thus complicating pulse by pulse efforts to quantify the number of photons. Improvements in counting the photons in each pulse have defined the state of the art for XAS sensitivity. Here we demonstrate a final step in these improvements through a balanced detection method that approaches the photon counting shot noise limit. In doing so, we obtain high quality absorption spectra from the insulator-metal transition in VO$_2$ and unlock a method to explore dilute systems, subtle processes and nonlinear phenomena with ultrafast x-rays. The method is especially beneficial for x-ray light sources where integration and averaging are not viable options to improve sensitivity.

Superconductivity and charge density waves (CDW) are competitive, yet coexisting orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scales is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa$_{2}$Cu$_{3}$O$_{6+x}$ following the quench of superconductivity by an infrared laser pulse. We observe a non-thermal response of the CDW order characterized by a near doubling of the correlation length within $\approx$ 1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDW manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations., Comment: Accepted version. 34 pages, 11 figures, Main text and Supplementary Materials

A topological concern is addressed in view of the extensively and intensively studied topological phases of condensed matter. In this realm, the phases with topological order cannot be characterized by symmetry alone. Moreover, the relevant phase transitions do occur without spontaneous symmetry breaking, beyond the scope of Landau's theory. The first realization of such phases is the discovery of the integer quantum Hall effect (QHE), which was followed soon by a topological interpretation. Later on, a distinct, half-integer QHE was also found from graphene, which has almost spin degeneracy described by $SU(2)$ symmetry. The previous theoretical predictions were realized in this finding. It has been well understood that the anomaly of this half-integer QHE originates from the presence of $2$D massless Dirac fermions around the zero energy with respect to the original Dirac points (DPs). The very characteristic lies in that there exists a topologically robust zero-mode LL that is a constant function of the perpendicular magnetic field. More deeply, this zero-mode LL is protected by the local chiral symmetry (CS), against CS preserving perturbations provided that intervalley scattering between the double DPs is inhibited, where the CS arises from the global sublattice symmetry in spinless graphene. Since massless Dirac particles are broadly present in condensed matter with various symmetries, not to mention Dirac bosonic systems, it is of interest to see how about the situations in other systems with $2$D massless Dirac fermions. We address several notes in a topological viewpoint on the presence of $2$D massless Dirac fermions in $3$D layered systems.In particular, we focus on the zero-mode LL since this LL signifies $2$D massless Dirac fermions.

We explore the rich and unique magnetic quantization of Si-doped graphene defect systems with various concentrations and configurations using the generalized tight-binding model. This model takes into account simultaneously the non-uniform bond lengths, site energies and hopping integrals, and a uniform perpendicular magnetic field (${B_z\hat z}$). The magnetic quantized Landau levels (LLs) are classified into four different kinds based on the probability distributions and oscillation modes. The main characteristics of LLs are clearly reflected in the magneto-optical selection rules which cover the dominating ${\Delta\,n=|n^v-n^c|=0}$, the coexistent ${\Delta\,n=0}$ $\&$ ${\Delta\,n=1}$, and the specific ${\Delta\,n=1}$. These rules for inter-LLs excitations come from the non-equivalence or equivalence of the A$_i$ and B$_i$ sublattices in a supercell.

The metal atoms, the alkali ones excepted, might provide the multiple outermost orbitals for the multi-orbital hybridizations with the out-of-plane $\pi$ bondings on the honeycomb lattice. This will dominate the fundamental properties of Al-, Ti- and Bi-adsorbed graphene nanoribbons, in which they are explored thoroughly by using the first-principles calculations. The principle focuses are the adatom-dependent binding energies, the adatom-carbon lengths, the optimal position, the maximum adatom concentrations, the free electron density transferred per adatom, the adatom-related valence and conduction bands, the various van Hove singularities in DOSs, the transition-metal-induced magnetic properties, and the significant competitions of the zigzag edge carbons and the metal/transition metal adatoms in spin configurations. The distinct chemical bondings are clearly identified from three kinds of metal adatoms under the delicate physical quantities. The important differences between Al-/Ti-/Bi- and alkali-adsorbed graphene nanoribbons will be discussed in detail, covering band structures, relation of conduction electron density and adatom concentration, spatial charge distributions, orbital-decomposed DOSs, and magnetic configurations $\&$ moments.

The generalized tight-binding model has been developed to thoroughly explore the essential electronic and optical properties of AB-bt bilayer silicene. They are greatly diversified by the buckled structure, stacking configuration, intralayer and interlayer hopping integrals, spin-orbital couplings; electric and magnetic fields (${E_z\hat z}$ $\&$ ${B_z\hat z}$). There exist the linear, parabolic and constant-energy-loop dispersions, multi-valley band structure and semiconductor-metal transition as $E_z$ varies. The $E_z$-dependent magnetic quantization exhibits the rich and unique Landau Levels (LLs) and magneto-optical spectra. The LLs have the lower degeneracy, valley-created localization centers, unusual distributions of quantum numbers, well-behaved and abnormal energy spectra in $B_z$-dependences, and the absence of anti-crossing behavior. A lot of pronounced magneto-absorption peaks occur at a very narrow frequency range, being attributed to diverse excitation categories. They have no specific selection rules except that the Dirac-cone band structures are driven by the critical electric fields. The optical gaps are reduced by $E_z$, but enhanced by $B_z$, in which the threshold channel might dramatically change in the formed case. The above-mentioned characteristics are in sharp contrast with those of layered graphenes., Comment: 39 pages, 12 figures

This review work addresses the recent advances in solving more comprehensive Hamiltonians. The generalized tight-binding model is developed to investigate the feature-rich quantization phenomena in emergent 2D materials. The mutli-orbital bondings, the spin-orbital interactions, the various geometric structures, and the external fields are taken into consideration simultaneously. Specifically, the IV-group layered systems, black phosphorus and MoS$_{2}$ exhibit the unique magnetic quantization. This is clearly indicated in three kinds of Landau levels (LLs), the orbital-, spin- and valley-dependent LL groups, the abnormal LL energy spectra, and the splitting, crossing and anticrossing behaviors. A detailed comparison with the effective-mass model is made. Some theoretical predictions have been confirmed by the experimental measurements., Comment: 25 pages, 20 figures

How to form carbon nanoscrolls with the non-uniform curvatures is worthy of a detailed investigation. The first-principles method is suitable in studying the combined effects due to the finite-size confinement, the edge-dependent interactions, the interlayer atomic interactions, the mechanical strains, and the magnetic configurations. The complex mechanisms can induce the unusual essential properties, e.g., the optimal structures, magnetisms, band gaps and energy dispersions. To reach a stable spiral profile, the requirements on the critical nanoribbon width and overlapping length will be thoroughly explored by evaluating the $W$-dependent scrolling energies. A comparison of formation energy between armchair and zigzag nanoscrolls is useful in understanding the experimental characterizations. The spin-up and spin-down distributions near the zigzag edges are examined for their magnetic environments. This accounts for the conservation or destruction of spin degeneracy. The various curved surfaces on a relaxed nanoscroll will create the complicated multi-orbital hybridizations, so that the low-lying energy dispersions and energy gaps are expected to be very sensitive to ribbon width, especially for those of armchair systems. Finally, the planar, curved, folded, scrolled graphene nanoribbons are compared with one another to illustrate the geometry-induced diversity., Comment: For major modification to this manuscript

Germanene nanoribbons, with buckled structures, exhibit unique electronic properties. The complicated relations among the quantum confinement, the spin-orbital coupling, the magnetic quantization, the electric-field dominated quantum numbers, energy dispersions, energy gap, state degeneracy, and wave functions. Such mechanisms can diversify spatial charge distributions and spin configurations on distinct sublattices. There exist the spin-split quasi-Landau levels and the valley-dependent asymmetric energy spectrum in a composite electric and magnetic field, manly owing to the destruction of z=0 mirror symmetry. The rich electronic structures are revealed in density of states as a lot of special structures. The predicted results could be directly verified by the scanning tunneling spectroscopy.

In this paper, we predict the existence of low-frequency nonlocal plasmon excitations at the vacuum-surface interface of a superlattice of $N$ graphene layers interacting with a thick conducting substrate. This is different from graphite which allows inter-layer hopping. A dispersion function is derived which incorporates the polarization function of the graphene monolayers (MLGs) and the dispersion function of a semi-infinite electron liquid at whose surface the electrons scatter specularly. We find that this surface plasmon-polariton is not damped by the particle-hole excitations (PHE's) or the bulk modes and separates below the continuum mini-band of bulk plasmon modes. For a conducting substrate with surface plasmon frequency $\omega_s=\omega_p/\sqrt{2}$, the surface plasmon frequency of the hybrid structure always lies below $\omega_s$. The intensity of this mode depends on the distance of the graphene layers from the surface of the conductor, the energy band gap between the valence and conduction bands of MLG and, most importantly, on the number of two-dimensional (2D) layers. Furthermore, the hybrid structure has no surface plasmon for a sufficiently large number ($N\stackrel{>}{\sim} 7$) of layers. The existence of two plasmons with different dispersion relations indicates that quasiparticles with different group velocity may coexist for various ranges of wavelength which is determined by the number of layers in the superlattice.

The geometric and electronic properties of Bi-adsorbed monolayer graphene, enriched by the strong effect of substrate, are investigated by first-principles calculations. The six-layered substrate, corrugated buffer layer, and slightly deformed monolayer graphene are all simulated. Adatom arrangements are thoroughly studied by analyzing the ground-state energies, bismuth adsorption energies, and Bi-Bi interaction energies of different adatom heights, inter-adatom distance, adsorption sites, and hexagonal positions. A hexagonal array of Bi atoms is dominated by the interactions between the buffer layer and the monolayer graphene. An increase in temperature can overcome a $\sim 50$ meV energy barrier and induce triangular and rectangular nanoclusters. The most stable and metastable structures agree with the scanning tunneling microscopy measurements. The density of states exhibits a finite value at the Fermi level, a dip at $\sim -0.2$ eV, and a peak at $\sim -0.6$ eV, as observed in the experimental measurements of the tunneling conductance.

The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like one by the rearrangement of many basis functions; furthermore, the spatial distributions of wave functions on distinct sublattices are utilized to largely reduce the numerical computation time. The external fields have a strong influence on the number, intensity, frequency and structure of absorption peaks, and the selection rules. The optical spectra in a uniform magnetic field exhibit plentiful symmetric absorption peaks and obey a specific selection rule. However, there are many asymmetric peaks and extra selection rules under the modulated electric field, the modulated magnetic field, the composite electric and magnetic fields, and the composite magnetic fields., Comment: 68 pages and 21 figures

We develop the tight-binding model to study electronic and optical properties of graphane. The strong sp3 chemical bondings among the carbon and hydrogen atoms induce a special band structure and thus lead to the rich optical excitations. The absorption spectrum hardly depends on the direction of electric polarization. It ex- hibits a lot of shoulder structures and absorption peaks, which arise from the extreme points and the saddle points of the parabolic bands, respectively. The threshold op- tical excitations, only associated with the 2px and 2py orbitals of the carbon atoms, are revealed in a shoulder structure at ?3.5 eV. The first symmetric absorption peak, appearing at ~11 eV, corresponds to energy bands due to the considerable hybridiza- tion of carbon 2pz orbitals and H 1s orbitals. Also, some absorption peaks at higher frequencies indicate the bonding of 2s and 1s orbitals. These results are in sharp contrast to those of the sp2 graphene systems., Comment: 16 pages, 5 figures

We study an SU(3) gauge theory with Nf=8 degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate and electroweak S parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the Nf=8 spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do not strongly disfavor the hypothesis of mass-deformed infrared conformality. Compared to Nf=2 we observe a significant enhancement of the chiral condensate relative to the symmetry breaking scale F, similar to the situation for Nf=6. The reduction of the S parameter, related to parity doubling in the vector and axial-vector channels, is also comparable to our six-flavor results.

The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the modulated one accounts for a strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules that are subsequently induced can be explained. When the modulated field increases, each symmetric peak, under a uniform magnetic field, splits into a pair of asymmetric peaks with lower intensities. The threshold absorption frequency exhibits an obvious evolution in terms of a redshift. These absorption peaks obey the same selection rule that is followed by Landau level transitions. Moreover, at a sufficiently strong modulation strength, the extra peaks in the absorption spectrum might arise from different selection rules.

We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of the Markov-chain Monte Carlo time series. This technique is expected to be particularly useful in situations where relatively few tunneling events are observed. Restriction to a lattice subvolume on which topological charge is not quantized is explored, and may lead to further improvement when the global topology is poorly sampled. We test our proposed method on a set of lattice data, and compare it to traditional methods., Comment: 7 pages, 6 figures. v2: update to published version

Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived non-perturbatively from the Schrodinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in non-supersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior., Comment: six pages, 4 figures

Composite dark matter candidates, which can arise from new strongly-coupled sectors, are well-motivated and phenomenologically interesting, particularly in the context of asymmetric generation of the relic density. In this work, we employ lattice calculations to study the electromagnetic form factors of electroweak-neutral dark-matter baryons for a three-color, QCD-like theory with Nf = 2 and 6 degenerate fermions in the fundamental representation. We calculate the (connected) charge radius and anomalous magnetic moment, both of which can play a significant role for direct detection of composite dark matter. We find minimal Nf dependence in these quantities. We generate mass-dependent cross-sections for dark matter-nucleon interactions and use them in conjunction with experimental results from XENON100, excluding dark matter candidates of this type with masses below 10 TeV., Comment: 8 pages, 5 figures. v2: update to journal version

Optical selection rules for one-dimensional graphene nanoribbons are analytically studied and clarified based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of wavefunctions, can account for the selection rules, which depend on the edge structure of nanoribbon, namely armchair or zigzag edges. The selection rule of armchair nanoribbons is \Delta J=0, and the optical transitions occur from the conduction to valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |\Delta J|=odd, which results from the alternatively changing symmetry property as the subband index increases. An efficiently theoretical prediction on transition energies is obtained with the application of selection rules. Furthermore, the energies of band edge states become experimentally attainable via optical measurements.

We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing $a$, ($a^{-1}$=\,1.73\,(3)\,GeV and $a^{-1}$=\,2.28\,(3)\,GeV). On the coarser lattice, with $24^3\times 64\times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3\times 64\times 16$ lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420\,MeV (225--420\,MeV for partially quenched pions). We use the masses of the $\pi$ and $K$ mesons and the $\Omega$ baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include $f_\pi=124(2)_{\rm stat}(5)_{\rm syst}$\,MeV, $f_K/f_\pi=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(96.2\pm 2.7)$\,MeV and $m_{ud}^{\bar{\textrm{MS}}}(2\,\textrm{GeV})=(3.59\pm 0.21)$\,MeV\, ($m_s/m_{ud}=26.8\pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[\Sigma^{\msbar}(2 {\rm GeV})]^{1/3} = 256(6)\; {\rm MeV}$, where $\Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$\,fm and $r_1=0.333(9)$\,fm., Comment: 129 pages, 59 figures, Published version containing an extended discussion of reweighting and including a new appendix (Appendix C)

We present the recent high-statistics calculations of the nucleon electromagnetic form factors with fully dynamical domain wall fermions on the 32^3x64 lattices generated by the RBC and UKQCD collaborations, with pion masses at roughly 297 MeV, 355 MeV and 403 MeV. We study the phenomenological fits to the momentum transfer dependence of the form factors and investigate chiral extrapolations for the Dirac radius, Pauli radius and the anomalous magnetic moment using two variants of chiral effective field theories, the small scale expansion (SSE) and covariant baryon chiral perturbation theory., Comment: Talk given at the XXVII International Symposium on Lattice Field Theory, Beijing, China, July 26-31, 2009. 8 pages, 9 figures

We study the region of the QCD phase transition using 2+1 flavors of domain wall fermions (DWF) and a $16^3 \times 8$ lattice volume with a fifth dimension of $L_s = 32$. The disconnected light quark chiral susceptibility, quark number susceptibility and the Polyakov loop suggest a chiral and deconfining crossover transition lying between 155 and 185 MeV for our choice of quark mass and lattice spacing. In this region the lattice scale deduced from the Sommer parameter $r_0$ is $a^{-1} \approx 1.3$ GeV, the pion mass is $\approx 300$ MeV and the kaon mass is approximately physical. The peak in the chiral susceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV where the first error is associated with determining the peak location and the second with our unphysical light quark mass and non-zero lattice spacing. The effects of residual chiral symmetry breaking on the chiral condensate and disconnected chiral susceptibility are studied using several values of the valence $L_s$., Comment: 41 pages, 10 tables, 13 figures

We present a high-statistics calculation of nucleon electromagnetic form factors in $N_f=2+1$ lattice QCD using domain wall quarks on fine lattices, to attain a new level of precision in systematic and statistical errors. Our calculations use $32^3 \times 64$ lattices with lattice spacing a=0.084 fm for pion masses of 297, 355, and 403 MeV, and we perform an overdetermined analysis using on the order of 3600 to 7000 measurements to calculate nucleon electric and magnetic form factors up to $Q^2 \approx$ 1.05 GeV$^2$. Results are shown to be consistent with those obtained using valence domain wall quarks with improved staggered sea quarks, and using coarse domain wall lattices. We determine the isovector Dirac radius $r_1^v$, Pauli radius $r_2^v$ and anomalous magnetic moment $\kappa_v$. We also determine connected contributions to the corresponding isoscalar observables. We extrapolate these observables to the physical pion mass using two different formulations of two-flavor chiral effective field theory at one loop: the heavy baryon Small Scale Expansion (SSE) and covariant baryon chiral perturbation theory. The isovector results and the connected contributions to the isoscalar results are compared with experiment, and the need for calculations at smaller pion masses is discussed., Comment: 44 pages, 40 figures

We present initial calculations of nucleon matrix elements of twist-two operators with 2+1 flavors of domain wall fermions at a lattice spacing a = 0.084 fm for pion masses down to 300 MeV. We also compare the results with the domain wall calculations on a coarser lattice., Comment: 7 pages, 10 figures. Talks presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19 2008, Williamsburg, Virginia, USA

Low-energy Landau levels of AB-stacked zigzag graphene ribbons in the presence of a uniform perpendicular magnetic field (\textbf{B}) are investigated by the Peierls coupling tight-binding model. State energies and associated wave functions are dominated by the \textbf{B}-field strength and the $k_z$-dependent interribbon interactions. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level. Many doubly degenerate Landau levels and singlet curving magnetobands exist along $k_x$ and $k_z$ directions, respectively. Such features are directly reflected in density of states, which exhibits a lot of asymmetric prominent peaks because of 1D curving bands. The $k_z$-dependent interribbon interactions dramatically modify the magnetobands, such as the lift of double degeneracy, the change of state energies, and the production of two groups of curving magnetobands. They also change the characteristics of the wave functions and cause the redistribution of the charge carrier density. The $k_z$-dependent wave functions are further used to predict the selection rule of the optical transition., Comment: 17 pages, 9 figures

In order to advance lattice calculations of moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon to a new level of precision, this work investigates several key aspects of precision lattice calculations. We calculate the number of configurations required for constant statistical errors as a function of pion mass, describe the coherent sink method to help achieve these statistics, examine the statistical correlations between separate measurements, study correlations in the behavior of form factors at different momentum transfer, examine volume dependence, and compare mixed action results with those using comparable dynamical domain wall configurations. We also show selected form factor results and comment on the QCD evolution of our calculations of the flavor non-singlet nucleon angular momentum., Comment: 13 pages, 17 figures. Talks presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19 2008, Williamsburg, Virginia, USA

The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a field could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. There exist infinite Fermi-momentum states in sharply contrast with two crossing points (Dirac points) for graphene without external fields. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states., Comment: 12pages, 5 figures

We calculate results for K to pi and K to 0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low energy constants of the chiral effective theory can be determined. The low energy constants of these matrix elements are necessary for an understanding of the Delta I=1/2 rule, and for calculations of epsilon'/epsilon using current lattice QCD simulations., Comment: 43 pages, 2 figures, uses RevTeX, added and updated references

We calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size $L \approx 2.5$\texttt{fm}, and a lattice spacing of $a \approx 0.124$\texttt{fm}, for pion masses as light as $m_\pi \approx 300$\texttt{MeV}, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two- and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the three-flavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU(3) fits are inconsistent with their phenomenological values. Next-to-next-to-leading order SU(2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in $m_\pi$ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior., Comment: version published in PRD, 41 pages, 16 figures, 20 tables

We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {\rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $\Omega$ baryon, and the $\pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_\pi = 124.1(3.6)_{\rm stat}(6.9)_{\rm syst} {\rm MeV}$, $f_K = 149.6(3.6)_{\rm stat}(6.3)_{\rm syst} {\rm MeV}$ and $f_K/f_\pi = 1.205(0.018)_{\rm stat}(0.062)_{\rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $\bar{\rm MS}$ we find $ m_{ud}^{\bar{\rm MS}}(2 {\rm GeV}) = 3.72(0.16)_{\rm stat}(0.33)_{\rm ren}(0.18)_{\rm syst} {\rm MeV}$ and $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$., Comment: 133 pages, 25 figures

We present results for the nucleon axial charge g_A at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16^3x32 and 24^3x64lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_\pi is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m_\pi= 330 MeV. We also find that g_A exhibits a scaling with the single variable m_\pi L which can also be seen in previous two-flavor domain wall and Wilson fermion calculati ons. Using this scaling to eliminate the finite-volume effect, we obtain g_A = 1.20(6)(4) at the physical pion mass, m_\pi = 135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when V\ge (2.4 fm)^3. We argue this is a dynamical quark effect., Comment: 4 pages and 3 figures

We present results for meson masses and decay constants measured on 24^3x64 lattices using the domain wall fermion formulation with an extension of the fifth dimension of L_s=16 for N_f=2+1 dynamical quark flavors. The lightest dynamical meson mass in our set-up is around 331 MeV, while partially quenched mesons reach masses as low as 250 MeV. The applicability of SU(3)xSU(3) and SU(2)xSU(2) (partially quenched) chiral perturbation theory will be compared and we quote values for the low-energy constants from both approaches. We will extract the average light quark and strange quark masses and use a non-perturbative renormalization technique (RI/MOM) to quote their physical values. The pion and kaon decay constants are determined at those values from our chiral fits and their ratio is used to obtain the CKM-matrix element |V_us|. The results presented here include statistical errors only., Comment: 14 pages, 6 figures, 3 tables, joint proceedings for talks presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany

A monolayer graphene exists in an environment where a uniform magnetic field interacts a spatially modulated magnetic field. The spatially modulated magnetic field could affect Landau levels due to a uniform magnetic field. The modulation effects on Landau levels are investigated through the Peierl's tight-binding model. The magneto-electronic properties are dominated by the period, the strength, and the direction of a spatially modulated magnetic field. Such a field could induce the growth in dimensionality, the change of energy dispersions, the destroy of state degeneracy, and the creation of band-edge states. There are a robust Landau level at Fermi level and 1D parabolic subbands located around the original Landau levels, which make density of states exhibit a delta-function-like structure and many pairs of asymmetric peak structure, respectively. The density of states and the energies of band-edge states strongly depend on the strength, but not on the period and the direction., Comment: 11 pages,4 figures

The Peierl's tight-binding model, with the band Hamiltonian matrix, is used to calculate the magnetoelectronic structure of a monolayergraphite. There are many flat Landau levels and some oscillatory Landau levels. The low Landau-level energies are characterized by a simple relation, not for others. State degeneracy is, respectively, fourfold degenerate and doubly degenerate at low and high energies. The level spacing declines quickly and then grows gradually in the increase of state energy. The main features of electronic properties are directly reflected in density of states. The predicted results could be verified by the optical spectroscopy., Comment: 9 pages and 4 figures

We present the first results for neutral kaon mixing using 2+1 flavors of domain wall fermions. A new approach is used to extrapolate to the physical up and down quark masses from our numerical studies with pion masses in the range 240 -- 420 MeV; only $SU(2)_L \times SU(2)_R$ chiral symmetry is assumed and the kaon is not assumed to be light. Our main result is $B_K^{\bar{\rm MS}}(2 \mathrm{GeV}) = 0.524(10)(28)$ where the first error is statistical and the second incorporates estimates for all systematic errors., Comment: 4 pages, 4 figures. RBC and UKQCD collaborations

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with 2+1 dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a 16^3\times32 lattice, which amounts to a spatial volume of (2 fm)^3 in physical units. The number of sites in the fifth dimension is 16, which gives m_{res} = 0.00308(4) in these simulations. Three values of input light sea quark masses, m_l^{sea} \approx 0.85 m_s, 0.59 m_s and 0.33 m_s were used to allow for extrapolations to the physical light quark limit, whilst the heavier sea quark mass was fixed to approximately the physical strange quark mass m_s. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that f_\pi = 127(4) MeV, f_K = 157(5) MeV and f_K/f_\pi = 1.24(2), where the errors are statistical only, which are in good agreement with the experimental values., Comment: RBC and UKQCD Collaborations. 17 pages, 14 figures. Typeset with ReVTEX4. v2: replaced with the version published in PRD with improved introduction

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the $s$ quark, and two degenerate dynamical flavours with input bare masses ranging from $m_s$ to $m_s/4$ approximating the $u$ and $d$ quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on $16^3\times32$ lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large residual masses and a limited number of sea quark mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurements within our statistical uncertainties., Comment: RBC and UKQCD Collaborations. 82 pages, 34 figures Typos corrected