Destroying a topological quantum bit by condensing Ising vortices

The imminent realization of topologically-protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbors what is known as a Z$_2$ liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called {\it spinons}, or Ising flux vortices called {\it visons}. At zero temperature a Z$_2$ liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum phase transition destroying the topological order. In this paper, we use quantum Monte Carlo to study a vison-induced transition from a Z$_2$ liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is controlled by a new universality class beyond the standard Landau paradigm.Comment: 5 pages, 4 figures. Published versio

A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states for Stochastic Series Expansion QMC allowing a direct calculation of Renyi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.Comment: 9 pages, 7 figure

Geometric mutual information at classical critical points

A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to $c$. This makes it possible to extract $c$ in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models.Comment: 5 pages. v3: published versio

Movement demands and running intensities of semi-professional rugby league players in a 9’s tournament

The objective of the study was to describe the movement demands and running intensities of semi-professional rugby league players during a rugby league 9’s (RL9’s) tournament. Six semi-professional rugby league players competed in a RL9’s tournament over a two-day period comprising of six games. Movement demands and running intensities were recorded using Global Positioning System (GPS) devices providing data on distance and speeds. Data is presented as mean (95% Confidence Intervals) with changes (≥ 75%) likely to exceed the smallest worthwhile change (0.2) considered practically important. Outside backs performed significantly (p 2.0) decreases in performance variables were observed over the two days. The biggest magnitude of change over the two days was seen with very large decreases in relative HSR (- 2.10) and sprint (- 2.14) distance. Between playing groups, the outside backs had the biggest decrease in running intensity with a very large (- 2.32) significant (p < 0.05) decrease in VHSR on day 2 (3.3 m∙min-1 [2.5 – 4.1]) compared to day 1 (4.9 m∙min-1 [4.4 – 5.4]). Running intensities are de-creased during an intensified RL9’s tournament in semi-professional rugby league players. The observed decreases in running performances between playing groups are in agreement with previous research and may support the use of individualized player monitoring and recovery management during a RL9’s tournament-style competition