Multifractals Competing with Solitons on Fibonacci Optical Lattice

We study the stationary states for the nonlinear Schr\"odinger equation on the Fibonacci lattice which is expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are called critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions, a forbidden region, the spectrum of critical states, and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact irrespective of the nonlinearity in the sea of a large number of stationary solitons.Comment: 5 pages, 4 figures, major revision, references adde

Momentum space topology of fermion zero modes on brane

We discuss fermion zero modes within the 3+1 brain -- the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime, or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.Comment: LaTeX file, 8 pages, no figures, version accepted in JETP Letter

Dirac Nodes and Quantized Thermal Hall Effect in the Mixed State of d-wave Superconductors

We consider the vortex state of d-wave superconductors in the clean limit. Within the linearized approximation the quasiparticle bands obtained are found to posess Dirac cone dispersion (band touchings) at special points in the Brillouin zone. They are protected by a symmetry of the linearized Hamiltonian that we call T_Dirac. Moreover, for vortex lattices that posess inversion symmetry, it is shown that there is always a Dirac cone centered at zero energy within the linearized theory. On going beyond the linearized approximation and including the effect of the smaller curvature terms (that break T_Dirac), the Dirac cone dispersions are found to acquire small gaps (0.5 K/Tesla in YBCO) that scale linearly with the applied magnetic field. When the chemical potential for quasiparticles lies within the gap, quantization of the thermal-Hall conductivity is expected at low temperatures i.e. kappa_{xy}/T = n[(pi k_B)^2/(3h)] with the integer `n' taking on values n=+2, -2, 0. This quantization could be seen in low temperature thermal transport measurements of clean d-wave superconductors with good vortex lattices.Comment: (23 pages in all [7 pages in appendices], 9 figures

Quasi-periodic spin chains in a magnetic field

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-1/2 XXZ chain. A new class of magnetization plateaux are obtained by means of Abelian bosonization methods which give rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.Comment: 4 pages RevTeX, 5 PostScript figures included. Final version to appear in PR

Deconfinement and the Hagedorn Transition in String Theory

Superseded and extended in hep-th/0105110 and hep-th/0208112.Comment: Superseded and extended in hep-th/0105110 and hep-th/020811

Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.

Disturbance spreading in incommensurate and quasiperiodic systems

The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances $\sigma^2(t)$ of atom displacements depends on the initial condition. For the initial condition with nonzero momentum, $\sigma^2(t)$ goes as $t^\alpha$ with $\alpha=1$ and 0 for incommensurate Frenkel-Kontorova (FK) model at $V$ below and above $V_c$ respectively; and $\alpha=1$ for uniform, quasiperiodic and random chains. It is also found that $\alpha=1-\beta$ with $\beta$ the exponent of distribution function of frequency at zero frequency, i.e., $\rho(\omega)\sim \omega^{\beta}$ (as $\omega\to 0$). For the initial condition with zero momentum, $\alpha=0$ for all systems studied. The underlying physical meaning of this diffusive behavior is discussed.Comment: 8 Revtex Pages, 5 PS figures included, to appear in Phys. Rev. B April 200