Abstracts

The physics of interacting anyonic chains
Eddy Ardonne, Nordita

The study of anyonic quantum spin chains has revealed that these chains have a remarkable rich structure, which is governed by a so-called topological symmetry. The role of this topological symmetry on the various gapped and critical phases will be discussed, as well as the nucleation of novel topological phases.

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Adiabatic Gate Teleportation On Topological Quantum Systems
Dave Bacon, Washington

Adiabatic gate teleportation is a simple protocol for performing universal quantum computing by adiabatically deforming between Hamiltonians whose energy eigenstates are simple quantum error correcting codewords. Here I will discuss this protocol as well as its extension to simple topological models. This later extension will allow for rigorous exploration of the robustness of topological quantum computing models during computation, a subject of some recent controversy.

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Quantum Walks with Anyons: Decoherence by Knots
Gavin Brennen, Macquarie University

Quantum walks describe coherent dynamics which are distinct from classical random walks (e.g. quadratic vs. linear dispersion) but reducing to classical walks in the presence of decoherence. I will describe quantum walks with anyonic particles on a disk. The fusion degrees of freedom of non-Abelian anyons act as an environment which ``entangles'' the walkers trajectory with a knot in the world lines of the anyons and the degree of decoherence is quantified by evaluating link invariants for the quantum group representation of the anyons. Limits toward classical and quantum walk behavior will be discussed.

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Quantum double lattice models from Hopf algebras, and tensor networks
Oliver Buerschaper, Max Planck Institute of Quantum Optics

We show how to extend quantum double lattice models to certain non-trivial Hopf algebras and derive tensor network representations for their ground states. We analyze the structure of these tensor networks and relate them to other examples with topological order obtained from string-net models.

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An Introduction to the Theory of Incompressible Quantum Hall Fluids (tutorial)
Jürg Fröhlich, ETH Zurich

As suggested by several people, incompressible Hall fluids exhibiting quasi-particles with non-abelain braid statistics - assuming they can be realized - may be systems that can be used for topological quantum computing, although they will not take the form of "laptops", any time soon. In this lecture, I will present a short summary of a theory of incompressible Hall fluids that I have been involved in developing. I will recall what incompressible Hall fluids are and how to characterize their main physical properties. Subsequently, I will outline a general classification of such fluids. The special example of Hall fluids with a filling factor of 5/2 will be considered in more detail. Some remarks about quantum Hall interferometry will be made. Applications to topological quantum computing will be left to other speakers.

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Some basics of CFT (tutorial)
Matthias Gaberdiel, ETH Zurich

I will give a basic introduction to 2-dimensional conformal field theory with a particular emphasis on explaining the structure of WZW models.

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A stabilized solution to Kitaev's Honeycomb model
Graham Kells, National University of Ireland, Maynooth

In this talk I will discuss a new solution to Kitaev's honeycomb lattice model , see arXiv:0903.5211 (http://arxiv.org/abs/0903.5211). The method of solution is by fermionization through a Jordan-Wigner type transform that has been adapted from perturbative methods used to analyse the Abelian phase. Specifically I will show that the ground-state of the system, valid in both Abelian and non-Abelian phases, is a BCS condensate of fermion pairs over a toric code vacuum state with the same vorticity. This constitutes a complete closed form expression for the system ground-state and clearly illustrates the relationship between Abelian and non-Abelian phases in the system. A brief discussion of the ground-state degeneracy on a torus will also be given and I will discuss the mechanism by which the non-Abelian phase becomes 3-fold degenerate.

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Interaction driven phase transitions in an exactly solvable model
Ville Lahtinen, University of Leeds

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Non-abelian states in the fractional quantum Hall effect: present status
Rudolf Morf, Paul Scherrer Institute

We review some of the theoretical proposals for non-abelian fractional quantum Hall (FQH) states. We discuss which ones may be realizable in experimental systems and discuss recent experimental and theoretical results which make us hopeful in the case of the \nu=5/2 FQH state. We also review recent numerical results for a possible non-abelian state at \nu=12/5.

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Why should anyone care about computing with anyons?
Jiannis Pachos, University of Leeds

Two dimensional topological models appear in strongly correlated quantum systems that support anyons, vortex-like quasiparticles with classical and quantum properties. They are coupled to each other by effective gauge theories that give rise to their exotic statistics. After a brief overview of anyonic systems we will look in detail how such vortices can emerge in an exactly solvable lattice model.

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Hierarchical Hall states for the second Landau level
Joost Slingerland, Dublin IAS/NUI Maynooth

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Fractional topological insulators
Ady Stern, Weizmann Institute

We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with fractional charge and statistics in addition to protected edge modes. In the case of s^z conserving toy models, we show that a system is a fractional topological insulator if and only if \sigma_{sH}/e^* is odd, where \sigma_{sH} is the spin-Hall conductance in units of e/2\pi, and e^* is the elementary charge in units of e. We find that systems with 1/e^* even cannot support fractional topological insulators.

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Collective states of interacting anyons, edge states, and the nucleation of topological liquids
Simon Trebst, Microsoft Station Q

Interactions mediated by quasiparticle tunneling split the degenerate space of states formed by a set of localized, non-Abelian anyons in two spatial dimensions. Here we show that this splitting selects a unique collective state as new ground states and results in the nucleation of a novel gapped quantum liquid inside the original parent liquid (of which the anyons are excitations). The nucleated liquid is separated from the parent liquid by a neutral, chiral edge state which we characterize. This physics is at play for non-Abelian quantum Hall states o the center of the plateau.