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

Tensor product representations of the quantum double of a compact group

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the action of the R-matrix, and their decomposition into irreducible *-representations. The example of D(SU(2)) is treated in detail, with explicit formulas for direct integral decomposition (`Clebsch-Gordan series') and Clebsch-Gordan coefficients. We point out possible physical applications.Comment: LaTeX2e, 27 pages, corrected references, accepted by Comm.Math.Phy

More on core instabilities of magnetic monopoles

In this paper we present new results on the core instability of the 't Hooft Polyakov monopoles we reported on before. This instability, where the spherical core decays in a toroidal one, typically occurs in models in which charge conjugation is gauged. In this paper we also discuss a third conceivable configuration denoted as ``split core'', which brings us to some details of the numerical methods we employed. We argue that a core instability of 't Hooft Polyakov type monopoles is quite a generic feature of models with charged Higgs particles.Comment: Latex, 15 pages, 6 figures; published versio

On Sibling and Exceptional W Strings

We discuss the physical spectrum for $W$ strings based on the algebras $B_n$, $D_n$, $E_6$, $E_7$ and $E_8$. For a simply-laced $W$ string, we find a connection with the $(h,h+1)$ unitary Virasoro minimal model, where $h$ is the dual Coxeter number of the underlying Lie algebra. For the $W$ string based on $B_n$, we find a connection with the $(2h,2h+2)$ unitary $N=1$ super-Virasoro minimal model.Comment: 16 page

Spinor field realizations of the non-critical W2,4W_{2,4} string based on the linear W1,2,4W_{1,2,4} algebra

In this paper, we investigate the spinor field realizations of the $W_{2,4}$ algebra, making use of the fact that the $W_{2,4}$ algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the spinor non-critical $W_{2,4}$ string were built with these realizations.Comment: 10 pages, no figures, revtex4 style, accepted by Commun.Theor.Phy

Nested Topological Order

We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a gauge symmetry reduction mechanism. When symmetry is reduced in several islands only, this imposes boundary conditions to the rest of the system giving rise to topological ground state degeneracy. This degeneracy is related to the existence of topological fluxes in between islands or, alternatively, hidden charges at islands. Additionally, island deformations give rise to an extension of topological quantum computation beyond quasiparticles.Comment: revtex4, 4 page

Manipulating electronic states at oxide interfaces using focused micro X-rays from standard lab-sources

Recently, x-ray illumination, using synchrotron radiation, has been used to manipulate defects, stimulate self-organization and to probe their structure. Here we explore a method of defect-engineering low-dimensional systems using focused laboratory-scale X-ray sources. We demonstrate an irreversible change in the conducting properties of the 2-dimensional electron gas at the interface between the complex oxide materials LaAlO3 and SrTiO3 by X-ray irradiation. The electrical resistance is monitored during exposure as the irradiated regions are driven into a high resistance state. Our results suggest attention shall be paid on electronic structure modification in X-ray spectroscopic studies and highlight large-area defect manipulation and direct device patterning as possible new fields of application for focused laboratory X-ray sources.Comment: 12 pages, 4 figure

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

Assessing the environmental impacts of production- and consumption-side measures in sustainable agriculture intensification in the European Union

Sustainable agricultural intensification (SI) is an important strategy to respond to the combined challenge of achieving food security and providing public goods and ecosystem services to society, including mitigation and adaptation of climate change. Sustainable intensification includes a wide range of measures at both the supply and demand-side of agricultural production. However, currently, it is unclear what are the most effective and priority measures. This study assesses the potential of different SI measures for reducing GHG (greenhouse gas) emissions and increasing land use efficiency in the European Union's agriculture sector. A scenario approach was combined with life cycle analysis to quantify the environmental impacts of a number of different SI measures. The sustainable intensification measures assessed in this study are: 1) changing human diet; 2) using food waste in livestock diets; 3) shifting from monoculture cropping to crop rotation, and, 4) incorporating crop residues into the soil. The results reveal that the studied SI measures have the potential to increase land use savings, ranging from 0.06 to 3.32 m2/person/day, while GHG emission savings ranging from 71 to 1872 g CO2-eq/person/day can be achieved at EU level. Among these SI measures, changing human diet showed a remarkably high reduction of environmental impacts. On the contrary, increased GHG emission savings in the other SI measures (i.e. crop residue incorporation in the field and replacing soybean meal in conventional feed by food waste-based feed) are counter effected by increased GHG emissions in the energy sector due to reduction of feedstock availability for bioenergy production. The approach used in this study allows the assessment of both the production and consumption-side SI measures and allows the identification of the most effective SI measures and their potential trade-offs