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Spontaneous symmetry breaking from anyon condensation

  • Regular Article - Theoretical Physics
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  • Published: 12 February 2019
  • volume 2019, Article number: 62 (2019)
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Spontaneous symmetry breaking from anyon condensation
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  • Marcel Bischoff1,
  • Corey Jones2,
  • Yuan-Ming Lu  ORCID: orcid.org/0000-0001-6275-739X3 &
  • …
  • David Penneys2 
  • 662 Accesses

  • 11 Citations

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A preprint version of the article is available at arXiv.

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 G → EqBr(\( \mathcal{C} \)) such that g(A) ≅ A for all g ∈ G, 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.

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Authors and Affiliations

  1. Department of Mathematics, Ohio University, Morton Hall 321, 1 Ohio University, Athens, OH, 45701, U.S.A.

    Marcel Bischoff

  2. Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH, 43210, U.S.A.

    Corey Jones & David Penneys

  3. Department of Physics, The Ohio State University, 191 West Woodruff Ave, Columbus, OH, 43210, U.S.A.

    Yuan-Ming Lu

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  1. Marcel Bischoff
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Correspondence to Yuan-Ming Lu.

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ArXiv ePrint: 1811.00434

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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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  • Received: 08 November 2018

  • Accepted: 31 January 2019

  • Published: 12 February 2019

  • DOI: https://doi.org/10.1007/JHEP02(2019)062

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Keywords

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

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