Description
In (2+1)d, the transition from the Z_2 toric code phase to a trivial phase can be driven by the condensation of either the electric anyon e or magnetic anyon m. When the system has a global Z_2 “self-duality” symmetry that exchanges e and m anyons, the naive anyon-condensation picture no longer holds since e and m cannot simultaneously condense. Numerical studies have found a continuous transition from the toric code with the Z_2 self-duality symmetry to a trivial phase with the Z_2 spontaneously broken. Since then, a natural field-theoretic understanding of this transition has remained an open challenge. In this talk, I will propose an SO(4) Chern-Simons-Higgs (CSH) theory at level k=2 as a natural mean-field description of this self-dual transition. I will further show that varying the integer level k gives a broader series of analogous transitions involving non-Abelian topological orders, including the double Fibonacci order at k=3 and the S_3 quantum double at k=4.
https://arxiv.org/abs/2601.20945