Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect

We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling point contact system. We show that the non-symmetrized noise in the edge current for the system out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does not simply add up the equilibrium noise of the edge current. A correction term arises associated with the correlation between the tunnelling current and the edge current. We show, using a non-equilibrium Ward identity, that this correction term is determined by the anti-symmetric part of the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem and related expressions for the excess and shot noise of the noise in the edge current. Our approach makes use of simple properties of the edge, such as charge conservation and chirality, and applies to generic constructions of the edge theory which includes edges of non-Abelian states and edges with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.Comment: 20 pages, 5 figure

Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking

We describe a family of phase transitions connecting phases of differing non-trivial topological order by explicitly constructing Hamiltonians of the Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2+1 dimensions in terms of doubled Chern-Simons theories

Composite fermion model for entanglement spectrum of fractional quantum Hall states

We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states --- the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect --- can be very well described in terms of a simple model of non-interacting (or weakly interacting) composite fermions.Comment: 6 pages, 2 figure

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 $S$-matrix, also in the broken phase. From the measured broken $S$-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 $S$-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 $H=\bar{D_2}$ 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

Tunnelling current through fractional quantum Hall interferometers

We calculate the tunnelling current through a Fabry-P\'{e}rot interferometer in the fractional quantum Hall regime. Within linear response theory (weak tunnelling but arbitrary source-drain voltage) we find a general expression for the current due to tunnelling of quasiparticles in terms of Carlson's $R$ function. Our result is valid for fractional quantum Hall states with an edge theory consisting of a charged channel and any number of neutral channels, with possibly different edge velocities and different chiralities. We analyse the case with a single neutral channel in detail, which applies for instance to the edge of the Moore-Read state. In addition we consider an asymmetric interferometer with different edge lengths between the point contacts on opposite edges, and we study the behaviour of the current as a function of varying edge length. Recent experiments attempted to measure the Aharanov-Bohm effect by changing the area inside the interferometer using a plunger gate. Theoretical analyses of these experiments have so far not taken into account the accompanying change in the edge lengths. We show that the tunnelling current exhibits multiple osculations as a function of this edge length, with frequencies proportional to the injected edge current and inversely proportional to the edge velocities. In particular the edge velocities can be measured by looking at the Fourier spectrum of the edge current. We provide a numerical scheme to calculate and plot the $R$ function, and include sample plots for a variety of edge states with parameter values which are experimentally relevant.Comment: 30 pages, 14 figure

Topological Qubit Design and Leakage

We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Op- erations are performed on these by exchanging the anyons. One might argue that, in order to have as many simple single qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups which means they are valid for all anyon models. We also make some remarks on generalizations to other exchange groups.Comment: 13 pages, 3 figure

Evaluation of ranks of real space and particle entanglement spectra for large systems

We devise a way to calculate the dimensions of symmetry sectors appearing in the Particle Entanglement Spectrum (PES) and Real Space Entanglement Spectrum (RSES) of multi-particle systems from their real space wave functions. We first note that these ranks in the entanglement spectra equal the dimensions of spaces of wave functions with a number of particles fixed. This also yields equality of the multiplicities in the PES and the RSES. Our technique allows numerical calculations for much larger systems than were previously feasible. For somewhat smaller systems, we can find approximate entanglement energies as well as multiplicities. We illustrate the method with results on the RSES and PES multiplicities for integer quantum Hall states, Laughlin and Jain composite fermion states and for the Moore-Read state at filling $\nu=5/2$, for system sizes up to 70 particles.Comment: 5 pages, 2 figures; minor changes; New version includes the Real Space ES of Jain states; accepted for publication in Phys.Rev.Let

Comparison of Accu Chek Inform II point-of-care test blood glucose meter with Hexokinase Plasma method for a diabetes mellitus population during surgery under general anesthesia

Purpose Blood glucose (BG) concentrations of patients with diabetes mellitus (DM) are monitored during surgery to prevent hypo- and hyperglycemia. Access to point-of-care test (POCT) glucose meters at an operating room will usually provide monitoring at shorter intervals and may improve glycemic control. However, these meters are not validated for patients under general anesthesia. Methods This cross-sectional study included 75 arterial BG measurements from 75 patients (71 with DM, mostly insulin dependent) who underwent elective non-cardiac surgery under general anesthesia. Arterial blood samples were taken at least 60 minutes after induction. One drop of blood was used for Accu Chek Inform II (ACI II) POCT BG meter and the residual blood was sent to the clinical laboratory for a Hexokinase Plasma reference method. A Bland-Altman plot was used to visualize the differences between both methods, and correlation was assessed using the intra-class correlation coefficient (ICC). Results The results showed an estimated mean difference of 0.8 mmol/L between ACI II and the reference method, with limits of agreement equal to -0.6 and 2.2 mmol/L. In general, the reference method produced higher values than ACI II. ICC was 0.955 (95% CI 0.634-0.986), P &lt; 0.001, and concordance correlation coefficient (CCC) was 0.955 (95% CI 0.933-0.970). Conclusion Arterial BG measurements during surgery in patients with DM under general anesthesia using POCT BG meter are in general lower than laboratory measurements, but the ICC and CCC show a clinically acceptable correlation. We conclude that POCT measurements conducted on arterial specimens using the ACI II provide sufficiently accurate results for glucose measurement during surgery under general anesthesia.</p

Fourier transform and the Verlinde formula for the quantum double of a finite group

A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D(G). The Fourier transform relates the two ring structures. We use this to give a particularly short proof of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to appear in Journal of Physics

Determinants of HbA1c reduction with FreeStyle Libre flash glucose monitoring (FLARE-NL 5)

Aims: To identify factors predicting HbA1c reduction in patients with diabetes mellitus (DM) using FreeStyle Libre Flash Glucose Monitoring (FSL-FGM). Methods: Data from a 12-month prospective nation-wide FSL registry were used and analysed with multivariable regression. For the present study we included patients with hypoglycaemia unawareness or unexpected hypoglycaemias (n = 566) and persons who did not reach acceptable glycaemic control (HbA1c > 70 mmol/mol (8.5%)) (n = 294). People with other indications for use, such as sensation loss of the fingers or individuals already using FSL-FGM or rtCGM, were excluded (37%). Results: Eight hundred and sixty persons (55% male with a mean age of 46.7 (+/- 16.4) years) were included. Baseline HbA1c was 65.1 (+/- 14.5) mmol/mol (8.1 +/- 1.3%), 75% of the patients had type 1 DM and 37% had microvascular complications. Data concerning HbA1c was present for 482 (56.0%) at 6 months and 423 (49.2%) persons at 12 months. A significant reduction in HbA1c (>= 5 mmol/mol (0.5%)) was present in 187 (22%) persons. For these persons, median HbA1c reduction was -9.0 [-13.0, -4.0] mmol/mol (-0.82 [-1.19, -0.37]%) at 6 months and -9.0 [-15.0, -7.0] mmol/mol (-0.82 [-1.37, -0.64]%) at 12 months. In multi-variable regression analysis with age, gender and SF-12 physical and mental component scores as covariates, only baseline HbA1c was significant: -0.319 (SE 0.025; p <0.001; R-2 = 0.240 for the model). In exploratory analysis among subgroups with different indications for FSL-FGM use (hypoglycaemia unawareness or persistently high HbA1c) and persons with a significant HbA1c decrease over the study period, baseline HbA1c remained the only significant predictor. Conclusions: Among the variables we analysed in the present study, only high HbA1c at baseline predicts significant HbA1c reduction during FSL-CGM use