Quantum spin Hall effect and spin-charge separation in a kagome lattice

A two-dimensional kagome lattice is theoretically investigated within a simple tight-binding model, which includes the nearest neighbor hopping term and the intrinsic spin-orbit interaction between the next nearest neighbors. By using the topological winding properties of the spin-edge states on the complex-energy Riemann surface, the spin Hall conductance is obtained to be quantized as $-e/2\pi$ ($e/2\pi$) in insulating phases. This result keeps consistent with the numerical linear-response calculation and the \textbf{Z}$_{2}$ topological invariance analysis. When the sample boundaries are connected in twist, by which two defects with $\pi$ flux are introduced, we obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.Comment: 13 NJP pages, 7 figure

Modulation Equations: Stochastic Bifurcation in Large Domains

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations

Calculating critical temperatures of superconductivity from a renormalized Hamiltonian

It is shown that one can obtain quantitatively accurate values for the superconducting critical temperature within a Hamiltonian framework. This is possible if one uses a renormalized Hamiltonian that contains an attractive electron-electron interaction and renormalized single particle energies. It can be obtained by similarity renormalization or using flow equations for Hamiltonians. We calculate the critical temperature as a function of the coupling using the standard BCS-theory. For small coupling we rederive the McMillan formula for Tc. We compare our results with Eliashberg theory and with experimental data from various materials. The theoretical results agree with the experimental data within 10%. Renormalization theory of Hamiltonians provides a promising way to investigate electron-phonon interactions in strongly correlated systems.Comment: 6 pages, LaTeX, using EuroPhys.sty, one eps figure included, accepted for publication in Europhys. Let

Temperature in One-Dimensional Bosonic Mott insulators

The Mott insulating phase of a one-dimensional bosonic gas trapped in optical lattices is described by a Bose-Hubbard model. A continuous unitary transformation is used to map this model onto an effective model conserving the number of elementary excitations. We obtain quantitative results for the kinetics and for the spectral weights of the low-energy excitations for a broad range of parameters in the insulating phase. By these results, recent Bragg spectroscopy experiments are explained. Evidence for a significant temperature of the order of the microscopic energy scales is found.Comment: 8 pages, 7 figure

Symmetric Hyperbolic System in the Self-dual Teleparallel Gravity

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar formulation is posed. This system is different from the ones in other works by that the reality condition of the spatial metric is included in the symmetric hyperbolicity and then is no longer an independent condition. In addition the constraint equations of this system are rather simpler than the ones in other works.Comment: 8 pages, no figure

Tensor mass and particle number peak at the same location in the scalar-tensor gravity boson star models - an analytical proof

Recently in boson star models in framework of Brans-Dicke theory, three possible definitions of mass have been identified, all identical in general relativity, but different in scalar-tensor theories of gravity.It has been conjectured that it's the tensor mass which peaks, as a function of the central density, at the same location where the particle number takes its maximum.This is a very important property which is crucial for stability analysis via catastrophe theory. This conjecture has received some numerical support. Here we give an analytical proof of the conjecture in framework of the generalized scalar-tensor theory of gravity, confirming in this way the numerical calculations.Comment: 9 pages, latex, no figers, some typos corrected, reference adde

Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable

We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's parameter $\beta$. This generalized Lagrangian involves the chiral one as a special case of the value $\xi = \pm i$. We show that the generalized Lagrangian gives the canonical formulation of N = 1 SUGRA with the real Ashtekar variable after the 3+1 decomposition of spacetime. This canonical formulation is also derived from those of the usual N = 1 SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\beta (=\xi^{-1})$. We give some comments on the canonical formulation of the theory.Comment: 17 pages, LATE