100 research outputs found
Parafermion statistics and the application to non-abelian quantum Hall states
The (exclusion) statistics of parafermions is used to study degeneracies of
quasiholes over the paired (or in general clustered) quantum Hall states. Focus
is on the Z_k and su(3)_k/u(1)^2 parafermions, which are used in the
description of spin-polarized and spin-singled clustered quantum Hall states.Comment: 15 pages, minor changes, as publishe
Non-Abelian statistics in the interference noise of the Moore-Read quantum Hall state
We propose noise oscillation measurements in a double point contact,
accessible with current technology, to seek for a signature of the non-abelian
nature of the \nu=5/2 quantum Hall state. Calculating the voltage and
temperature dependence of the current and noise oscillations, we predict the
non-abelian nature to materialize through a multiplicity of the possible
outcomes: two qualitatively different frequency dependences of the nonzero
interference noise. Comparison between our predictions for the Moore-Read state
with experiments on \nu=5/2 will serve as a much needed test for the nature of
the \nu=5/2 quantum Hall state.Comment: 4 pages, 4 figures v2: typo's corrected, discussions clarified,
references adde
Non-abelian quantum Hall states - exclusion statistics, K-matrices and duality
We study excitations in edge theories for non-abelian quantum Hall states,
focussing on the spin polarized states proposed by Read and Rezayi and on the
spin singlet states proposed by two of the authors. By studying the exclusion
statistics properties of edge-electrons and edge-quasiholes, we arrive at a
novel K-matrix structure. Interestingly, the duality between the electron and
quasihole sectors links the pseudoparticles that are characteristic for
non-abelian statistics with composite particles that are associated to the
`pairing physics' of the non-abelian quantum Hall states.Comment: LaTeX2e, 40 page
Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting
We investigate a class of non-Abelian spin-singlet (NASS) quantum Hall
phases, proposed previously. The trial ground and quasihole excited states are
exact eigenstates of certain k+1-body interaction Hamiltonians. The k=1 cases
are the familiar Halperin Abelian spin-singlet states. We present closed-form
expressions for the many-body wave functions of the ground states, which for
k>1 were previously defined only in terms of correlators in specific conformal
field theories. The states contain clusters of k electrons, each cluster having
either all spins up, or all spins down. The ground states are non-degenerate,
while the quasihole excitations over these states show characteristic
degeneracies, which give rise to non-Abelian braid statistics. Using conformal
field theory methods, we derive counting rules that determine the degeneracies
in a spherical geometry. The results are checked against explicit numerical
diagonalization studies for small numbers of particles on the sphere.Comment: 17 pages, 4 figures, RevTe
Realizing All so(N)1 Quantum Criticalities in Symmetry Protected Cluster Models
We show that all so(N)1 universality class quantum criticalities emerge when
one-dimensional generalized cluster models are perturbed with Ising or Zeeman
terms. Each critical point is described by a low-energy theory of N linearly
dispersing fermions, whose spectrum we show to precisely match the prediction
by so(N)1 conformal field theory. Furthermore, by an explicit construction we
show that all the cluster models are dual to nonlocally coupled transverse
field Ising chains, with the universality of the so(N)1 criticality
manifesting itself as N of these chains becoming critical. This duality also
reveals that the symmetry protection of cluster models arises from the
underlying Ising symmetries and it enables the identification of local
representations for the primary fields of the so(N)1 conformal field theories.
For the simplest and experimentally most realistic case that corresponds to
the original one-dimensional cluster model with local three-spin interactions,
our results show that the su(2)2≃so(3)1 Wess-Zumino-Witten model can emerge in
a local, translationally invariant, and Jordan-Wigner solvable spin-1/2 model
Separation of spin and charge in paired spin-singlet quantum Hall states
We propose a series of paired spin-singlet quantum Hall states, which exhibit
a separation of spin and charge degrees of freedom. The fundamental excitations
over these states, which have filling fraction \nu=2/(2m+1) with m an odd
integer, are spinons (spin-1/2 and charge zero) or fractional holons (charge
+/- 1/(2m+1) and spin zero). The braid statistics of these excitations are
non-abelian. The mechanism for the separation of spin and charge in these
states is topological: spin and charge excitations are liberated by binding to
a vortex in a p-wave pairing condensate. We briefly discuss related, abelian
spin-singlet states and possible transitions.Comment: 4 pages, uses revtex
The structure of spinful quantum Hall states: a squeezing perspective
We provide a set of rules to define several spinful quantum Hall model
states. The method extends the one known for spin polarized states. It is
achieved by specifying an undressed root partition, a squeezing procedure and
rules to dress the configurations with spin. It applies to both the
excitation-less state and the quasihole states. In particular, we show that the
naive generalization where one preserves the spin information during the
squeezing sequence, may fail. We give numerous examples such as the Halperin
states, the non-abelian spin-singlet states or the spin-charge separated
states. The squeezing procedure for the series (k=2,r) of spinless quantum Hall
states, which vanish as r powers when k+1 particles coincide, is generalized to
the spinful case. As an application of our method, we show that the counting
observed in the particle entanglement spectrum of several spinful states
matches the one obtained through the root partitions and our rules. This
counting also matches the counting of quasihole states of the corresponding
model Hamiltonians, when the latter is available.Comment: 19 pages, 7 figures; v2: minor changes, and added references.
Mathematica packages are available for downloa
Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k
Using a form factor approach, we define and compute the character of the
fusion product of rectangular representations of \hat{su}(r+1). This character
decomposes into a sum of characters of irreducible representations, but with
q-dependent coefficients. We identify these coefficients as (generalized)
Kostka polynomials. Using this result, we obtain a formula for the characters
of arbitrary integrable highest-weight representations of \hat{su}(r+1) in
terms of the fermionic characters of the rectangular highest weight
representations.Comment: 21 pages; minor changes, typos correcte
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