18,829 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

### 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

### 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

### 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

### 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

### Fractional topological superconductors with fractionalized Majorana fermions

In this paper, we introduce a two-dimensional fractional topological
superconductor (FTSC) as a strongly correlated topological state which can be
achieved by inducing superconductivity into an Abelian fractional quantum Hall
state, through the proximity effect. When the proximity coupling is weak, the
FTSC has the same topological order as its parent state and is thus Abelian.
However, upon increasing the proximity coupling, the bulk gap of such an
Abelian FTSC closes and reopens resulting in a new topological order: a
non-Abelian FTSC. Using several arguments we will conjecture that the conformal
field theory (CFT) that describes the edge state of the non-Abelian FTSC is
$U(1)/Z_2$ orbifold theory and use this to write down the ground-state wave
function. Further, we predict FTSC based on the Laughlin state at $\nu=1/m$
filling to host fractionalized Majorana zero modes bound to superconducting
vortices. These zero modes are non-Abelian quasiparticles which is evident in
their quantum dimension of $d_m=\sqrt{2m}$. Using the multi-quasi-particle wave
function based on the edge CFT, we derive the projective braid matrix for the
zero modes. Finally, the connection between the non-Abelian FTSCs and the
$Z_{2m}$ rotor model with a similar topological order is illustrated.Comment: 15 pages, 2 figure

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