405 research outputs found
Anyons in a weakly interacting system
We describe a theoretical proposal for a system whose excitations are anyons
with the exchange phase pi/4 and charge -e/2, but, remarkably, can be built by
filling a set of single-particle states of essentially noninteracting
electrons. The system consists of an artificially structured type-II
superconducting film adjacent to a 2D electron gas in the integer quantum Hall
regime with unit filling fraction. The proposal rests on the observation that a
vacancy in an otherwise periodic vortex lattice in the superconductor creates a
bound state in the 2DEG with total charge -e/2. A composite of this
fractionally charged hole and the missing flux due to the vacancy behaves as an
anyon. The proposed setup allows for manipulation of these anyons and could
prove useful in various schemes for fault-tolerant topological quantum
computation.Comment: 7 pages with 3 figures. For related work and info visit
http://www.physics.ubc.ca/~fran
Laws of biology: why so few?
Finding fundamental organizing principles is the current intellectual front end of systems biology. From a hydrogen atom to the whole cell level, organisms manage massively parallel and massively interactive processes over several orders of magnitude of size. To manage this scale of informational complexity it is natural to expect organizing principles that determine higher order behavior. Currently, there are only hints of such organizing principles but no absolute evidences. Here, we present an approach as old as Mendel that could help uncover fundamental organizing principles in biology. Our approach essentially consists of identifying constants at various levels and weaving them into a hierarchical chassis. As we identify and organize constants, from pair-wise interactions to networks, our understanding of the fundamental principles in biology will improve, leading to a theory in biology
Fractional quantum Hall effect in the absence of Landau levels
It has been well-known that topological phenomena with fractional
excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982}
will emerge when electrons move in Landau levels. In this letter, we report the
discovery of the FQHE in the absence of Landau levels in an interacting fermion
model. The non-interacting part of our Hamiltonian is the recently proposed
topologically nontrivial flat band model on the checkerboard lattice
\cite{sun}. In the presence of nearest-neighboring repulsion (), we find
that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5
filling, however, a next-nearest-neighboring repulsion is needed for the
occurrence of the 1/5 FQHE when is not too strong. We demonstrate the
characteristic features of these novel states and determine the phase diagram
correspondingly.Comment: 6 pages and 4 figure
Quantum Hall Effect in a Holographic Model
We consider a holographic description of a system of strongly coupled
fermions in 2+1 dimensions based on a D7-brane probe in the background of
D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We
study the system at finite temperature and charge density, and in the presence
of a background magnetic field. We show that Minkowski-like embeddings that
terminate above the horizon describe a family of quantum Hall states with
filling fractions that are parameterized by a single discrete parameter. The
quantization of the Hall conductivity is a direct consequence of the
topological quantization of the fluxes. When the magnetic field is varied
relative to the charge density away from these discrete filling fractions, the
embeddings deform continuously into black-hole-like embeddings that enter the
horizon and that describe metallic states. We also study the thermodynamics of
this system and show that there is a first order phase transition at a critical
temperature from the quantum Hall state to the metallic state.Comment: v2: 27 pages, 12 figures. There is a major revision in the
quantitative analysis. The qualitative results and conclusions are unchanged,
with one exception: we show that the quantum Hall state embeddings, which
exist for discrete values of the filling fraction, deform continuously into
metallic state embeddings away from these filling fraction
From Rotating Atomic Rings to Quantum Hall States
Considerable efforts are currently devoted to the preparation of ultracold
neutral atoms in the emblematic strongly correlated quantum Hall regime. The
routes followed so far essentially rely on thermodynamics, i.e. imposing the
proper Hamiltonian and cooling the system towards its ground state. In rapidly
rotating 2D harmonic traps the role of the transverse magnetic field is played
by the angular velocity. For particle numbers significantly larger than unity,
the required angular momentum is very large and it can be obtained only for
spinning frequencies extremely near to the deconfinement limit; consequently,
the required control on experimental parameters turns out to be far too
stringent. Here we propose to follow instead a dynamic path starting from the
gas confined in a rotating ring. The large moment of inertia of the fluid
facilitates the access to states with a large angular momentum, corresponding
to a giant vortex. The initial ring-shaped trapping potential is then
adiabatically transformed into a harmonic confinement, which brings the
interacting atomic gas in the desired quantum Hall regime. We provide clear
numerical evidence that for a relatively broad range of initial angular
frequencies, the giant vortex state is adiabatically connected to the bosonic
Laughlin state, and we discuss the scaling to many particles.Comment: 9 pages, 5 figure
Emergent excitations in a geometrically frustrated magnet
Frustrated systems are ubiquitous and interesting because their behavior is
difficult to predict. Magnetism offers extreme examples in the form of spin
lattices where all interactions between spins cannot be simultaneously
satisfied. Such geometrical frustration leads to macroscopic degeneracies, and
offers the possibility of qualitatively new states of matter whose nature has
yet to be fully understood. Here we have discovered how novel composite spin
degrees of freedom can emerge from frustrated interactions in the cubic spinel
ZnCr2O4. Upon cooling, groups of six spins self-organize into weakly
interacting antiferromagnetic loops whose directors, defined as the unique
direction along which the spins are aligned parallel or antiparallel, govern
all low temperature dynamics. The experimental evidence comes from a
measurement of the magnetic form factor by inelastic neutron scattering. While
the data bears no resemblance to the atomic form factor for chromium, they are
perfectly consistent with the form factor for hexagonal spin loop directors.
The hexagon directors are to a first approximation decoupled from each other
and hence their reorientations embody the long-sought local zero energy modes
for the pyrochlore lattice.Comment: 10 pages, 4 figures upon reques
Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions
In contrast to classical physics, quantum mechanics divides particles into
two classes-bosons and fermions-whose exchange statistics dictate the dynamics
of systems at a fundamental level. In two dimensions quasi-particles known as
'anyons' exhibit fractional exchange statistics intermediate between these two
classes. The ability to simulate and observe behaviour associated to
fundamentally different quantum particles is important for simulating complex
quantum systems. Here we use the symmetry and quantum correlations of entangled
photons subjected to multiple copies of a quantum process to directly simulate
quantum interference of fermions, bosons and a continuum of fractional
behaviour exhibited by anyons. We observe an average similarity of 93.6\pm0.2%
between an ideal model and experimental observation. The approach generalises
to an arbitrary number of particles and is independent of the statistics of the
particles used, indicating application with other quantum systems and large
scale application.Comment: 10 pages, 5 figure
Spectral weight transfer in a disorder-broadened Landau level
In the absence of disorder, the degeneracy of a Landau level (LL) is
, where is the magnetic field, is the area of the sample
and is the magnetic flux quantum. With disorder, localized states
appear at the top and bottom of the broadened LL, while states in the center of
the LL (the critical region) remain delocalized. This well-known phenomenology
is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE)
[1]. One unnoticed issue is where the new states appear as the magnetic field
is increased. Here we demonstrate that they appear predominantly inside the
critical region. This leads to a certain ``spectral ordering'' of the localized
states that explains the stripes observed in measurements of the local inverse
compressibility [2-3], of two-terminal conductance [4], and of Hall and
longitudinal resistances [5] without invoking interactions as done in previous
work [6-8].Comment: 5 pages 3 figure
Paired and clustered quantum Hall states
We briefly summarize properties of quantum Hall states with a pairing or
clustering property. Their study employs a fundamental connection with
parafermionic Conformal Field Theories. We report on closed form expressions
for the many-body wave functions and on multiplicities of the fundamental
quasi-hole excitations.Comment: 13 pages, Contribution to the proceedings of the NATO Advanced
Research Workshop "Statistical Field Theories" Como (Italy), June 18-23 200
Multicomponent fractional quantum Hall effect in graphene
We report observation of the fractional quantum Hall effect (FQHE) in high
mobility multi-terminal graphene devices, fabricated on a single crystal boron
nitride substrate. We observe an unexpected hierarchy in the emergent FQHE
states that may be explained by strongly interacting composite Fermions with
full SU(4) symmetric underlying degrees of freedom. The FQHE gaps are measured
from temperature dependent transport to be up 10 times larger than in any other
semiconductor system. The remarkable strength and unusual hierarcy of the FQHE
described here provides a unique opportunity to probe correlated behavior in
the presence of expanded quantum degrees of freedom.Comment: 5 pages, 3 figure
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