Research

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  Non-invertible symmetry enriched string net topological orders
  

  Luisa Eck, Peter Huston, Kyle Kawagoe, and David Penneys

  We extend the theory of symmetry-enriched topological orders and their associated twist defects to non-invertible symmetries. The action of the non-invertible symmetry can be calculated using tube algebra methods and may map an anyon to a sum of anyons and twist defects.
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  3d conformal field theories via fuzzy sphere algebra
  

  Luisa Eck and Zhenghan Wang

  Fuzzy sphere regularizations of 3d CFTs are built from electron density operators projected to the lowest Landau level. We study the algebra of these density modes and its thermodynamic limits.
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  Dualities between 2+1d fusion surface models from braided fusion categories
  

  Luisa Eck

  We extend the fusion surface model construction so that the input is a pair (M,B), with M a module tensor category over the braided fusion category B. Models built from the same B are related by dualities / discrete gauging.
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  Generalizations of Kitaev's honeycomb model from braided fusion categories
  

  Luisa Eck, Paul Fendley

  We explore two-dimensional quantum lattice models constructed from braided fusion categories, which generalize Kitaev's honeycomb model. Their categorical 1-form symmetries make them promising candidates for chiral topological order.
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  From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
  

  Luisa Eck, Paul Fendley

  We discuss duality mappings between four different quantum lattice models, including the spin-1/2 XXZ chain and a model describing Rydberg-blockade atoms on a square ladder, as well as the non-invertible symmetries in these models.
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  Critical lines and ordered phases in the Rydberg-blockade ladder
  

  Luisa Eck, Paul Fendley

  We explore the phase diagram of the Rydberg-blockade ladder away from the integrable line and find different symmetry-broken and disordered phases together with first and second order phase transitions between them.