We consider the Ashkin-Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the ...extension that is necessary to prove a divergent susceptibility.
A model of strongly correlated spinless fermions hopping on a checkerboard lattice is mapped onto a quantum fully-packed loop model. We identify a large number of fluctuationless states specific to ...the fermionic case. We also show that for a class of fluctuating states, the fermionic sign problem can be gauged away. This claim is supported by numerically evaluating the energies of the low-lying states. Furthermore, we analyze in detail the excitations at the Rokhsar-Kivelson point of this model thereby using the relation to the height model and the single-mode approximation.
J. Stat. Phys., vol.94, (1999) p.53-66 The $q=2$ random cluster model is studied in the context of two mean field
models: The Bethe lattice and the complete graph. For these systems, the
critical ...exponents that are defined in terms of finite clusters have some
anomalous values as the critical point is approached from the high density side
which vindicates the results of earlier studies. In particular, the exponent
$\tilde \gamma^\prime$ which characterises the divergence of the average size
of finite clusters is 1/2 and $\tilde\nu^\prime$, the exponent associated with
the length scale of finite clusters is 1/4. The full collection of exponents
indicates an upper critical dimension of 6. The standard mean field exponents
of the Ising system are also present in this model ($\nu^\prime = 1/2$,
$\gamma^\prime = 1$) which implies, in particular, the presence of two
diverging length scales. Furthermore, the finite cluster exponents are stable
to the addition of disorder which, near the upper critical dimension, may have
interesting implications concerning the generality of the disordered
system/correlation length bounds.
The \(q=2\) random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of ...finite clusters have some anomalous values as the critical point is approached from the high density side which vindicates the results of earlier studies. In particular, the exponent \(\tilde \gamma^\prime\) which characterises the divergence of the average size of finite clusters is 1/2 and \(\tilde\nu^\prime\), the exponent associated with the length scale of finite clusters is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model (\(\nu^\prime = 1/2\), \(\gamma^\prime = 1\)) which implies, in particular, the presence of two diverging length scales. Furthermore, the finite cluster exponents are stable to the addition of disorder which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit ...of these exotic particles originated from Read and Green’s observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane’s construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
Understanding cellular architecture is essential for understanding biology. Electron microscopy (EM) uniquely visualizes cellular structures with nanometre resolution. However, traditional methods, ...such as thin-section EM or EM tomography, have limitations in that they visualize only a single slice or a relatively small volume of the cell, respectively. Focused ion beam-scanning electron microscopy (FIB-SEM) has demonstrated the ability to image small volumes of cellular samples with 4-nm isotropic voxels
. Owing to advances in the precision and stability of FIB milling, together with enhanced signal detection and faster SEM scanning, we have increased the volume that can be imaged with 4-nm voxels by two orders of magnitude. Here we present a volume EM atlas at such resolution comprising ten three-dimensional datasets for whole cells and tissues, including cancer cells, immune cells, mouse pancreatic islets and Drosophila neural tissues. These open access data (via OpenOrganelle
) represent the foundation of a field of high-resolution whole-cell volume EM and subsequent analyses, and we invite researchers to explore this atlas and pose questions.
Intracellular recording allows precise measurement and manipulation of individual neurons, but it requires stable mechanical contact between the electrode and the cell membrane, and thus it has ...remained challenging to perform in behaving animals. Whole-cell recordings in freely moving animals can be obtained by rigidly fixing ('anchoring') the pipette electrode to the head; however, previous anchoring procedures were slow and often caused substantial pipette movement, resulting in loss of the recording or of recording quality. We describe a UV-transparent collar and UV-cured adhesive technique that rapidly (within 15 s) anchors pipettes in place with virtually no movement, thus substantially improving the reliability, yield and quality of freely moving whole-cell recordings. Recordings are first obtained from anesthetized or awake head-fixed rats. UV light cures the thin adhesive layers linking pipette to collar to head. Then, the animals are rapidly and smoothly released for recording during unrestrained behavior. The anesthetized-patched version can be completed in ∼4-7 h (excluding histology) and the awake-patched version requires ∼1-4 h per day for ∼2 weeks. These advances should greatly facilitate studies of neuronal integration and plasticity in identified cells during natural behaviors.
Interferometry of non-Abelian anyons Bonderson, Parsa; Shtengel, Kirill; Slingerland, J.K.
Annals of physics,
11/2008, Letnik:
323, Številka:
11
Journal Article
Recenzirano
We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the ...basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach–Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach–Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore–Read state at
ν
=
5
/
2
and Read–Rezayi state at
ν
=
12
/
5
.
We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to fractional ...quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu = 12/5 plateau.
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