Classification of the anyon sectors of Kitaev's quantum double model

We give a complete classification of the anyon sectors of Kitaev's quantum double model on the infinite triangular lattice and for finite gauge group $G$, including the non-abelian case. As conjectured, the anyon sectors of the model correspond precisely to the irreducible representations of the quantum double algebra of $G$. Our proof consists of two main parts. In the first part, we construct for each irreducible representation of the quantum double algebra a pure state and show that the GNS representations of these pure states are pairwise disjoint anyon sectors. In the second part we show that any anyon sector is unitarily equivalent to one of the anyon sectors constructed in the first part. Purity of the states constructed in the first part is shown by characterising these states as the unique states that satisfy appropriate local constraints. These constraints are of two types, namely flux constraints and gauge constraints. The flux constraints single out certain string-net states, while the gauge constraints fix the way in which these string-nets condense. At the core of the proof is the fact that certain groups of local gauge transformations act freely and transitively on collections of local string-nets. The proof that the GNS representations of these states are anyon sectors relies on showing that they are unitarily equivalent to amplimorphism representations which are much easier to compare to the ground state representation. For the second part, we show that any anyon sector contains a pure state that satisfies all but a finite number of the constraints characterising the pure states of the first part. Using known techniques we can then construct a pure state in the anyon sector that satisfies all but one of these constraints. Finally, we show that any such state must be a vector state in one of the anyon sectors constructed in the first part.Comment: Errors of version 1 fixed, presentation throughout the manuscript improved. 83 pages, 16 figure

Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice

The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk, and has a nonvanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous

Fredholm Homotopies for Strongly-Disordered 2D Insulators

We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the context of these systems. We use this technique to prove the bulk-edge correspondence for mobility-gapped 2D topological insulators possessing a (Fermionic) time-reversal symmetry (class AII) and provide an alternative route to a theorem by Elgart-Graf-Schenker (2005) about the bulk-edge correspondence for strongly-disordered integer quantum Hall systems. We furthermore provide a proof of the stability of the $\mathbb{Z}_2$ index in the mobility gap regime. These two-dimensional results serve as a model for the study of higher dimensional $\mathbb{Z}_2$ indices.Comment: 21 pages, 2 figur

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Measurement of prompt open-charm production cross sections in proton-proton collisions at root s=13 TeV

The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb(-1). The differential production cross sections of the D*(+/-), D-+/-, and D-0 ((D) over bar (0)) mesons are presented in ranges of transverse momentum and pseudorapidity 4 < p(T) < 100 GeV and vertical bar eta vertical bar < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.Peer reviewe