Diagrammatics for Bose condensation in anyon theories

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.Comment: 20 pages, 1 figure, many diagram

Spin texture readout of a Moore-Read topological quantum register

We study the composite Charged Spin Texture (CST) over the Moore-Read quantum Hall state that arises when a collection of elementary CSTs are moved to the same location. Following an algebraic approach based on the characteristic pair correlations of the Moore-Read state, we find that the resulting CST is set by the fusion sector of the underlying non-Abelian quasiparticles. This phenomenon provides a novel way to read out the quantum register of a non-Abelian topologically ordered phase.Comment: 4 pages, 6 figure

Performance and behaviour of rabbit does in a group-housing system with natural mating or artificial insemination

This study compared reproductive performance and behaviour of does raised in a group-housing system and in a regular cage system. The group-housing pen was divided into different functional areas for suckling, resting, and eating and special hiding areas for kits when they had left the nest-boxes and does to favour the species specific behavioural traits. Does had access to their nest-box by means of an individual Electronic Nest-box Recognition System (ENRS) activated by a coded transponder placed in their eartags. Eight does were housed in each pen. Natural mating (NM, with a buck in the group) or artificial inseminations (AI) were applied. Litter size, kit mortality and kit weight at 14 d of age were similar for group-housing and cages when NM were applied. With a natural reproduction rhythm group-housing led to an increase of +38% of litters. However, from a management point of view, a cycled production system with AI is preferred. With AI and group-housing, a lower kindling rate and a lower kit weight at weaning were found. The lower kindling rate was partly caused by pseudo-pregnancies that were found in 23% (P < 0.01) of the does in the group-housing system against 0% in the control group. Sixteen to 20% of the does in the group-housing system had skin injuries, which is an indicator for aggression among does. Most of the injuries were seen on the body and most of them were superficial bites. Based on the results of this study, it can be concluded that group-housing of rabbit does seems possible, but more research is needed to solve the problems of the decreased kindling rate and occurrence of pseudo-pregnancies, the lower weight at weaning and aggressiveness among does

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

Focus on topological quantum computation

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches