41,233 research outputs found
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
A mean field approach for string condensed states
We describe a mean field technique for quantum string (or dimer) models.
Unlike traditional mean field approaches, the method is general enough to
include string condensed phases in addition to the usual symmetry breaking
phases. Thus, it can be used to study phases and phases transitions beyond
Landau's symmetry breaking paradigm. We demonstrate the technique with a simple
example: the spin-1 XXZ model on the Kagome lattice. The mean field calculation
predicts a number of phases and phase transitions, including a z=2 deconfined
quantum critical point.Comment: 10 pages + appendix, 15 figure
Quantum ether: photons and electrons from a rotor model
We give an example of a purely bosonic model -- a rotor model on the 3D cubic
lattice -- whose low energy excitations behave like massless U(1) gauge bosons
and massless Dirac fermions. This model can be viewed as a ``quantum ether'': a
medium that gives rise to both photons and electrons. It illustrates a general
mechanism for the emergence of gauge bosons and fermions known as ``string-net
condensation.'' Other, more complex, string-net condensed models can have
excitations that behave like gluons, quarks and other particles in the standard
model. This suggests that photons, electrons and other elementary particles may
have a unified origin: string-net condensation in our vacuum.Comment: 10 pages, 6 figures, RevTeX4. Home page http://dao.mit.edu/~we
Continuous topological phase transitions between clean quantum Hall states
Continuous transitions between states with the {\em same} symmetry but
different topological orders are studied. Clean quantum Hall (QH) liquids with
neutral quasiparticles are shown to have such transitions. For clean bilayer
(nnm) states, a continous transition to other QH states (including non-Abelian
states) can be driven by increasing interlayer repulsion/tunneling. The
effective theories describing the critical points at some transitions are
derived.Comment: 4 pages, RevTeX, 2 eps figure
Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian
Berry phases as we exchange quasiparticle excitations. In this paper, we
construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory.
We find that lattice dislocation defects in the model produce topologically
protected degeneracy. Even though dislocations are not quasiparticle
excitations, they resemble non-Abelian anyons with quantum dimension sqrt(N).
Exchanging dislocations can produces topologically protected projective
non-Abelian Berry phases. The dislocations, as projective non-Abelian anyons
can be viewed as a generalization of the Majorana zero modes.Comment: 4 pages + refs, 4 figures. RevTeX
Electronic height indicator for agricultural machines
This paper addresses the design and development of a low cost electronic height indicator for a self-propelled spray rig. The prime objective is to give a spray rig operator an accurate indication of the boom height above the ground by using an electronic display in the tractor cabin to improve the efficiency of chemical application. This indicator is implemented using a microcontroller and a Hall-effect sensor. The field test proves that this indicator has improved the spraying performance by eliminating human error in estimating boom height, especially during night-time and dusty conditions
Three-dimensional topological phase on the diamond lattice
An interacting bosonic model of Kitaev type is proposed on the
three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev
model on the honeycomb lattice which exhibits both Abelian and non-Abelian
phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak
pairing phase, the auxiliary Majorana hopping problem is in a topological
superconducting phase characterized by a non-zero winding number introduced in
A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The
topological character of the weak pairing phase is protected by a discrete
symmetry.Comment: 7 pages, 5 figure
Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
We find a series of possible continuous quantum phase transitions between
fractional quantum Hall (FQH) states at the same filling fraction in
two-component quantum Hall systems. These can be driven by tuning the
interlayer tunneling and/or interlayer repulsion. One side of the transition is
the Halperin (p,p,p-3) Abelian two-component state while the other side is the
non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition
is a continuous transition in the 3D Ising class. The critical point is
described by a Z2 gauged Ginzburg-Landau theory. These results have
implications for experiments on two-component systems at \nu = 2/3 and
single-component systems at \nu = 8/3.Comment: 4 pages + ref
Exterior splashes and linear sets of rank 3
In \PG(2,q^3), let be a subplane of order that is exterior to
\li. The exterior splash of is defined to be the set of
points on \li that lie on a line of . This article investigates
properties of an exterior \orsp\ and its exterior splash. We show that the
following objects are projectively equivalent: exterior splashes, covers of the
circle geometry , Sherk surfaces of size , and
\GF(q)-linear sets of rank 3 and size . We compare our construction
of exterior splashes with the projection construction of a linear set. We give
a geometric construction of the two different families of sublines in an
exterior splash, and compare them to the known families of sublines in a
scattered linear set of rank 3
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