132 research outputs found
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 of atom
displacements depends on the initial condition. For the initial condition with
nonzero momentum, goes as with and 0 for
incommensurate Frenkel-Kontorova (FK) model at below and above
respectively; and for uniform, quasiperiodic and random chains. It
is also found that with the exponent of distribution
function of frequency at zero frequency, i.e., (as ). For the initial condition with zero
momentum, 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
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