Filippa Getzner

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n nature, most particles can be classified as either bosons, described by symmetric wave functions, or fermions, described by antisymmetric wave functions. In two spacial dimensions, a third type of (quasi)particle can appear: the anyon, which is characterised by fractional exchange statistics. These quasiparticles can be viewed as excitations of fractional quantum Hall liquids and form the basis for topological quantum computation. In this talk, we focus on the almost bosonic anyon gas, which is described by a two-parameter Chern-Simons-Schrödinger energy functional. We discuss recent results showing that the low energy states of the model are well approximated by states of the nonlinear Landau levels (NLL), a family of soliton states parametrised by coprime and complex polynomials. The polynomials depend on the position of the zeros/vortices of the NLL states. Using these solutions, we derive explicit expressions for the Berry connection and compute Berry phases associated with adiabatic transport along closed loops in the parameter space given by vortex positions, scaling, and interaction terms. The results suggest a dependence of the resulting geometric phase on the topology of the underlying configuration space. More broadly, our work contributes to the understanding of geometric aspects of many-anyon systems whilst conceptually connecting to holonomic and topological quantum computation.

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Uppsala University & Ericsson
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Contact: Markus Heinrich