Gapless Fermions and Quantum Order

Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.Comment: 23 pages. LaTeX. Homepage http://dao.mit.edu/~we

Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows $(\lambda_t=\lambda ^l, l\ge0)$ from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given.Comment: 24 pages, LaTex, revise

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible multiphase flows

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulation are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic multiphase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.Comment: 9 Figure

A scheme for demonstration of fractional statistics of anyons in an exactly solvable model

We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their braiding operations, can be conveniently realized through \textit{dynamic}laser manipulation of cold atoms in an optical lattice. Due to the perfect localization of anyons in this model, we show that a quantum circuit with only six qubits is enough for demonstration of the basic braiding statistics of anyons. This opens up the immediate possibility of proof-of-principle experiments with trapped ions, photons, or nuclear magnetic resonance systems.Comment: 4 pages, 3 figure

Superconductivity in Ti-doped Iron-Arsenide Compound Sr4Cr0.8Ti1.2O6Fe2As2

Superconductivity was achieved in Ti-doped iron-arsenide compound Sr4Cr0.8Ti1.2O6Fe2As2 (abbreviated as Cr-FeAs-42622). The x-ray diffraction measurement shows that this material has a layered structure with the space group of \emph{P4/nmm}, and with the lattice constants a = b = 3.9003 A and c = 15.8376 A. Clear diamagnetic signals in ac susceptibility data and zero-resistance in resistivity data were detected at about 6 K, confirming the occurrence of bulk superconductivity. Meanwhile we observed a superconducting transition in the resistive data with the onset transition temperature at 29.2 K, which may be induced by the nonuniform distribution of the Cr/Ti content in the FeAs-42622 phase, or due to some other minority phase.Comment: 3 pages, 3 figure