Spontaneous symmetry breaking from anyon condensation

Abstract

In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the ground state. In the traditional Landau theory, a symmetry group can break down to any subgroup. However, this no longer holds across a continuous phase transition driven by anyon condensation in symmetry enriched topological orders (SETOs). For a SETO described by a G-crossed braided extension \( \mathcal{C}\subseteq {\mathcal{C}}_G^{\times } \), we show that physical considerations require that a connected étale algebra A\( \mathcal{C} \) admit a G-equivariant algebra structure for symmetry to be preserved under condensation of A. Given any categorical action GEqBr(\( \mathcal{C} \)) such that g(A) ≅ A for all gG, we show there is a short exact sequence whose splittings correspond to G-equivariant algebra structures. The non-splitting of this sequence forces spontaneous symmetry breaking under condensation of A, while inequivalent splittings of the sequence correspond to different SETOs resulting from the anyon-condensation transition. Furthermore, we show that if symmetry is preserved, there is a canonically associated SETO of \( {\mathcal{C}}_A^{\mathrm{loc}} \), and gauging this symmetry commutes with anyon condensation.

A preprint version of the article is available at ArXiv.

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Bischoff, M., Jones, C., Lu, YM. et al. Spontaneous symmetry breaking from anyon condensation. J. High Energ. Phys. 2019, 62 (2019). https://doi.org/10.1007/JHEP02(2019)062

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Keywords

  • Anyons
  • Spontaneous Symmetry Breaking
  • Topological Field Theories
  • Topological States of Matter