65 research outputs found
Search for electron liquids with non-Abelian quasiparticles
We use exact numerical diagonalization in the search of fractional quantum
Hall states with non-Abelian quasiparticle statistics. For the (most promising)
states in a partially filled second Landau level, the search is narrowed to the
range of filling factors . In this range, the analysis of
energy spectra and correlation functions, calculated including finite width and
Landau level mixing, supports the prominent non-Abelian candidates at
(paired Moore--Read "pfafian" state) and 12/5 (clustered
Read--Rezayi "parafermion" state). Outside of this range, the noninteracting
composite fermion model with four attached flux quanta is validated, yielding
the family of quantum liquids with fractional, but Abelian statistics. The
borderline state is shown to be adiabatically connected to the
Laughlin liquid, but its short-range correlations are significantly different.Comment: 9 pages, 8 figure
Real-Space Entanglement Spectrum of Quantum Hall States
We investigate the entanglement spectra arising from sharp real-space
partitions of the system for quantum Hall states. These partitions differ from
the previously utilized orbital and particle partitions and reveal
complementary aspects of the physics of these topologically ordered systems. We
show, by constructing one to one maps to the particle partition entanglement
spectra, that the counting of the real-space entanglement spectra levels for
different particle number sectors versus their angular momentum along the
spatial partition boundary is equal to the counting of states for the system
with a number of (unpinned) bulk quasiholes excitations corresponding to the
same particle and flux numbers. This proves that, for an ideal model state
described by a conformal field theory, the real-space entanglement spectra
level counting is bounded by the counting of the conformal field theory edge
modes. This bound is known to be saturated in the thermodynamic limit (and at
finite sizes for certain states). Numerically analyzing several ideal model
states, we find that the real-space entanglement spectra indeed display the
edge modes dispersion relations expected from their corresponding conformal
field theories. We also numerically find that the real-space entanglement
spectra of Coulomb interaction ground states exhibit a series of branches,
which we relate to the model state and (above an entanglement gap) to its
quasiparticle-quasihole excitations. We also numerically compute the
entanglement entropy for the nu=1 integer quantum Hall state with real-space
partitions and compare against the analytic prediction. We find that the
entanglement entropy indeed scales linearly with the boundary length for large
enough systems, but that the attainable system sizes are still too small to
provide a reliable extraction of the sub-leading topological entanglement
entropy term.Comment: 13 pages, 11 figures; v2: minor corrections and formatting change
Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
In this letter we propose an interferometric experiment to detect non-Abelian
quasiparticle statistics -- one of the hallmark characteristics of the
Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The
implications for using this state for constructing a topologically protected
qubit as has been recently proposed by Das Sarma et. al. are also addressed.Comment: 5 pages, 2 eps figures v2: A few minor changes and citation
corrections. In particular, the connection to cond-mat/9711087 has been
clarified. v3: Minor changes: fixed references to Fig. 2, updated citations,
changed a few words to conform to the version published in PR
Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states
Utilizing large-scale Monte-Carlo simulations, we investigate an
unconventional two-component classical plasma in two dimensions which controls
the behavior of the norms and overlaps of the quantum-mechanical wavefunctions
of Ising-type quantum Hall states. The plasma differs fundamentally from that
which is associated with the two-dimensional XY model and Abelian fractional
quantum Hall states. We find that this unconventional plasma undergoes a
Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal.
The parameter values corresponding to Ising-type quantum Hall states lie on the
metallic side of this transition. This result verifies the required properties
of the unconventional plasma used to demonstrate that Ising-type quantum Hall
states possess quasiparticles with non-Abelian braiding statistics.Comment: 16 pages, 14 figures. Submitted to Physical Review
Coulomb Blockade Doppelgangers in Quantum Hall States
In this paper, we ask the question: How well can Coulomb blockade experiments
correctly identify and distinguish between different topological orders in
quantum Hall states? We definitively find the answer to be: Quite poorly. In
particular, we write the general expression for the spacing of resonance peaks
in a simple form that explicitly displays its dependence on the conformal
scaling dimensions of the systems' edge modes. This form makes transparent the
general argument that the Coulomb blockade peak spacings do not provide a
strongly indicative signature of the topological order of the system, since it
is only weakly related to the braiding statistics. We bolster this general
argument with examples for all the most physically relevant non-Abelian
candidate states, demonstrating that they have Coulomb blockade doppelgangers
-- candidate states at the same filling fraction with identical Coulomb
blockade signatures, but dramatically different topological orders and braiding
statistics.Comment: 12 pages, 1 figure; portions of this paper were formerly included in
Appendix C of arXiv:0903.3108; v2: examples added, minor corrections made;
v3: discussions of non-uniform filling and of hierarchical counterparts of
multi-component states added, minor corrections mad
Optimal confinement potential in quantum Hall droplets
We find that the confinement potential of a few electron quantum dot can be
tuned to significantly increase the overlap with certain quantum Hall trial
wave functions. Besides manipulating inter-electron interaction, this approach
may prove useful in quantum point contact experiments, which involve narrow
constrictions.Comment: 4 pages, 1 figur
Clebsch-Gordan and 6j-coefficients for rank two quantum groups
We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two
quantum groups. We explain in detail how such calculations are done, which
should allow the reader to perform similar calculations in other cases.
Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as
well as some other topological data associated with theories corresponding to
rank-two quantum groups. Finally, we collect some useful properties of the
fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica
notebooks containing the various q-CG and 6j symbols, see
http://arxiv.org/src/1004.5456/an
Decay Modes of Unstable Strings in Plane-Wave String Field Theory
The cubic interaction vertex of light-cone string field theory in the
plane-wave background has a simple effective form when considering states with
only bosonic excitations. This simple effective interaction vertex is used in
this paper to calculate the three string interaction matrix elements for states
of arbitrary bosonic excitation and these results are used to examine certain
decay modes on the mass-shell. It is shown that the matrix elements of one
string to two string decays involving only bosonic excitations will vanish to
all orders in 1/mu on the mass-shell when the number of excitations on the
initial string is less than or equal to two, but in general will not vanish
when the number of excitations is greater than two. Also, a truncated
calculation of the mass-shell matrix elements for one string to three string
decays of two excitation states is performed and suggests that these matrix
elements do not vanish on the mass-shell. There is, however, a quantitative
discrepancy between this last result and its (also non-vanishing) gauge theory
prediction from the BMN correspondence.Comment: 11 pages; v2: references added; v3: normalization of interaction
vertex and corresponding amplitudes changed by a factor of mu to reflect SFT
normalization (must now divide by mu to compare with BMN dual gauge theory),
and minor errors correcte
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Non-Abelian statistics and topological quantum information processing in 1D wire networks
Topological quantum computation provides an elegant way around decoherence,
as one encodes quantum information in a non-local fashion that the environment
finds difficult to corrupt. Here we establish that one of the key
operations---braiding of non-Abelian anyons---can be implemented in
one-dimensional semiconductor wire networks. Previous work [Lutchyn et al.,
arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving
semiconducting wires into a topological phase supporting long-sought particles
known as Majorana fermions that can store topologically protected quantum
information. Majorana fermions in this setting can be transported, created, and
fused by applying locally tunable gates to the wire. More importantly, we show
that networks of such wires allow braiding of Majorana fermions and that they
exhibit non-Abelian statistics like vortices in a p+ip superconductor. We
propose experimental setups that enable the Majorana fusion rules to be probed,
along with networks that allow for efficient exchange of arbitrary numbers of
Majorana fermions. This work paves a new path forward in topological quantum
computation that benefits from physical transparency and experimental realism.Comment: 6 pages + 17 pages of Supp. Mat.; 10 figures. Supp. Mat. has doubled
in size to establish results more rigorously; many other improvements as wel
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