Review of integrable anyonic chains with new examples identified for su(2)_k, Tambara-Yamagami TY(Z_n), Fib x Fib, Fib x Ising, and preliminary results for Haagerup-Izumi categories.
Russian doll spectrum in a non-Abelian string-net ladder
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abstract
We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark constrast with the ones obtained for Fibonacci or Ising theories.
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Constrained integrability and anyonic chains
Review of integrable anyonic chains with new examples identified for su(2)_k, Tambara-Yamagami TY(Z_n), Fib x Fib, Fib x Ising, and preliminary results for Haagerup-Izumi categories.