Non-Abelian statistics as a Berry phase in exactly solvable models

We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.Comment: 10 pages, 3 figures. To appear in New Journal of Physic

Field Tuning of Ferromagnetic Domain Walls on Elastically Coupled Ferroelectric Domain Boundaries

We report on the evolution of ferromagnetic domain walls during magnetization reversal in elastically coupled ferromagnetic-ferroelectric heterostructures. Using optical polarization microscopy and micromagnetic simulations, we demonstrate that the spin rotation and width of ferromagnetic domain walls can be accurately controlled by the strength of the applied magnetic field if the ferromagnetic walls are pinned onto 90 degrees ferroelectric domain boundaries. Moreover, reversible switching between magnetically charged and uncharged domain walls is initiated by magnetic field rotation. Switching between both wall types reverses the wall chirality and abruptly changes the width of the ferromagnetic domain walls by up to 1000%.Comment: 5 pages, 5 figure

Scaling Properties of Random Walks on Small-World Networks

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in $d$-dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.Comment: 7 pages, 8 figures, two-column format. Submitted to PR

Informing Non-Response Bias Model Creation in Social Surveys with Visualisation

Through an ongoing process of co-design and co-discovery we are developing and using visualization to explore large amounts of auxiliary data from unfamiliar sources to understand non-response bias in social surveys. We present auxiliary data in their geographical contexts and show how this can complement traditional data analysis and provide a more comprehensive understanding of the data. This is helping select variables for non-response modelling. These processes are not just limited to non-response analysis, but have potential to be used in wider quantitative analysis in social science

Solution of voter model dynamics on annealed small-world networks

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $\tau$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $\tau$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.Comment: 11 pages, 4 figures, published version. Added section with extension to generic number of nearest neighbor

Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.Comment: 9 pages, 9 figure

Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator

Recently a pair of experiments demonstrated a simulation of Abelian anyons in a spin network of single photons. The experiments were based on an Abelian discrete gauge theory spin lattice model of Kitaev. Here we describe how to use linear optics and single photons to simulate non-Abelian anyons. The scheme makes use of joint qutrit-qubit encoding of the spins and the resources required are three pairs of parametric down converted photons and 14 beam splitters.Comment: 13 pages, 5 figures. Several references added in v