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TUT: Tutorials

TUT 5: Tutorial: Correlations in Integrable Quantum Many-Body Systems (TT)

TUT 5.2: Tutorium

Sonntag, 6. März 2016, 16:45–17:30, H20

Non-Abelian anyons — •Holger Frahm — Institut für Theoretische Physik, Leibniz Universität Hannover

In this tutorial we shall discuss the construction and analysis of integrable many-body quantum systems built from non-Abelian anyons -- objects with most exotic statistics under permutation whose states are protected against local perturbations by the existence of topological charges. They can appear as quasi-particle excitations in certain topological quantum liquids and are possibly realized in quantum Hall states at certain fractional filling factors or frustrated two-dimensional quantum magnets. Integrable models can provide unbiased insights into the nature of the collective states of many anyons formed in the presence of interactions.

We begin the tutorial with a brief review of the theoretical description of interacting many-anyon lattice models starting from the underlying fusion category. Within this framework a basis of operators for local interactions of anyons as well as the topological charges characterizing the many-anyon state are built. Finally, we show how by fine-tuning of the coupling constants the resulting models can be embedded into families of commuting operators and discuss strategies for the calculation of their spectral properties.