Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude

We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling anaysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read-Rezayi Z_k-parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit nontrivial k-dependent corrections to the scaling exponent.Comment: 16 pages, 4 figure

Ground state and edge excitations of quantum Hall liquid at filling factor 2/3

We present a numerical study of fractional quantum Hall liquid at Landau level filling factor $\nu=2/3$ in a microscopic model including long-range Coulomb interaction and edge confining potential, based on the disc geometry. We find the ground state is accurately described by the particle-hole conjugate of a $\nu=1/3$ Laughlin state. We also find there are two counter-propagating edge modes, and the velocity of the forward-propagating mode is larger than the backward-propagating mode. The velocities have opposite responses to the change of the background confinement potential. On the other hand changing the two-body Coulomb potential has qualitatively the same effect on the velocities; for example we find increasing layer thickness (which softens of the Coulomb interaction) reduces both the forward mode and the backward mode velocities.Comment: 12 pages, 13 figure

Improving Ant Collaborative Filtering on Sparsity via Dimension Reduction

Recommender systems should be able to handle highly sparse training data that continues to change over time. Among the many solutions, Ant Colony Optimization, as a kind of optimization algorithm modeled on the actions of an ant colony, enjoys the favorable characteristic of being optimal, which has not been easily achieved by other kinds of algorithms. A recent work adopting genetic optimization proposes a collaborative filtering scheme: Ant Collaborative Filtering (ACF), which models the pheromone of ants for a recommender system in two ways: (1) use the pheromone exchange to model the ratings given by users with respect to items; (2) use the evaporation of existing pheromone to model the evolution of users’ preference change over time. This mechanism helps to identify the users and the items most related, even in the case of sparsity, and can capture the drift of user preferences over time. However, it reveals that many users share the same preference over items, which means it is not necessary to initialize each user with a unique type of pheromone, as was done with the ACF. Regarding the sparsity problem, this work takes one step further to improve the Ant Collaborative Filtering’s performance by adding a clustering step in the initialization phase to reduce the dimension of the rate matrix, which leads to the results that K<<#users, where K is the number of clusters, which stands for the maximum number of types of pheromone carried by all users. We call this revised version the Improved Ant Collaborative Filtering (IACF). Experiments are conducted on larger datasets, compared with the previous work, based on three typical recommender systems: (1) movie recommendations, (2) music recommendations, and (3) book recommendations. For movie recommendation, a larger dataset, MoviesLens 10M, was used, instead of MoviesLens 1M. For book recommendation and music recommendation, we used a new dataset that has a much larger size of samples from Douban and NetEase. The results illustrate that our IACF algorithm can better deal with practical recommendation scenarios that handle sparse dataset

The Universal Edge Physics in Fractional Quantum Hall Liquids

The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been unambiguously observed in experiments in two-dimensional electron gases based on GaAs/GaAlAs heterostructures or quantum wells. One plausible cause is the fractional quantum Hall edge reconstruction, which introduces non-chiral edge modes. The coupling between counterpropagating edge modes can modify the exponent of the $I$-$V$ characteristics. By comparing the $\nu=1/3$ fractional quantum Hall states in modulation-doped semiconductor devices and in graphene devices, we show that the graphene-based systems have an experimental accessible parameter region to avoid the edge reconstruction, which is suitable for the exploration of the universal edge tunneling exponent predicted by the chiral Luttinger liquid theory.Comment: 7 pages, 6 figure