Journal of High Energy Physics

, 2019:62 | Cite as

Spontaneous symmetry breaking from anyon condensation

  • Marcel Bischoff
  • Corey Jones
  • Yuan-Ming LuEmail author
  • David Penneys
Open Access
Regular Article - Theoretical Physics


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.


Anyons Spontaneous Symmetry Breaking Topological Field Theories Topological States of Matter 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of MathematicsOhio UniversityAthensU.S.A.
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusU.S.A.
  3. 3.Department of PhysicsThe Ohio State UniversityColumbusU.S.A.

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