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 n...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2019)062 |
| _version_ | 1811314072676728832 |
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| author | Marcel Bischoff Corey Jones Yuan-Ming Lu David Penneys |
| author_facet | Marcel Bischoff Corey Jones Yuan-Ming Lu David Penneys |
| author_sort | Marcel Bischoff |
| collection | DOAJ |
| description | 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 C ⊆ C G × $$ \mathcal{C}\subseteq {\mathcal{C}}_G^{\times } $$ , we show that physical considerations require that a connected étale algebra A ∈ C $$ \mathcal{C} $$ admit a G-equivariant algebra structure for symmetry to be preserved under condensation of A. Given any categorical action G → EqBr( C $$ \mathcal{C} $$ ) 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 C A l o c $$ {\mathcal{C}}_A^{\mathrm{loc}} $$ , and gauging this symmetry commutes with anyon condensation. |
| first_indexed | 2024-04-13T11:05:24Z |
| format | Article |
| id | doaj.art-5848c7152029405eb234327a72c9f0ef |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T11:05:24Z |
| publishDate | 2019-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5848c7152029405eb234327a72c9f0ef2022-12-22T02:49:17ZengSpringerOpenJournal of High Energy Physics1029-84792019-02-012019214210.1007/JHEP02(2019)062Spontaneous symmetry breaking from anyon condensationMarcel Bischoff0Corey Jones1Yuan-Ming Lu2David Penneys3Department of Mathematics, Ohio UniversityDepartment of Mathematics, The Ohio State UniversityDepartment of Physics, The Ohio State UniversityDepartment of Mathematics, The Ohio State UniversityAbstract 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 C ⊆ C G × $$ \mathcal{C}\subseteq {\mathcal{C}}_G^{\times } $$ , we show that physical considerations require that a connected étale algebra A ∈ C $$ \mathcal{C} $$ admit a G-equivariant algebra structure for symmetry to be preserved under condensation of A. Given any categorical action G → EqBr( C $$ \mathcal{C} $$ ) 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 C A l o c $$ {\mathcal{C}}_A^{\mathrm{loc}} $$ , and gauging this symmetry commutes with anyon condensation.http://link.springer.com/article/10.1007/JHEP02(2019)062AnyonsSpontaneous Symmetry BreakingTopological Field TheoriesTopological States of Matter |
| spellingShingle | Marcel Bischoff Corey Jones Yuan-Ming Lu David Penneys Spontaneous symmetry breaking from anyon condensation Journal of High Energy Physics Anyons Spontaneous Symmetry Breaking Topological Field Theories Topological States of Matter |
| title | Spontaneous symmetry breaking from anyon condensation |
| title_full | Spontaneous symmetry breaking from anyon condensation |
| title_fullStr | Spontaneous symmetry breaking from anyon condensation |
| title_full_unstemmed | Spontaneous symmetry breaking from anyon condensation |
| title_short | Spontaneous symmetry breaking from anyon condensation |
| title_sort | spontaneous symmetry breaking from anyon condensation |
| topic | Anyons Spontaneous Symmetry Breaking Topological Field Theories Topological States of Matter |
| url | http://link.springer.com/article/10.1007/JHEP02(2019)062 |
| work_keys_str_mv | AT marcelbischoff spontaneoussymmetrybreakingfromanyoncondensation AT coreyjones spontaneoussymmetrybreakingfromanyoncondensation AT yuanminglu spontaneoussymmetrybreakingfromanyoncondensation AT davidpenneys spontaneoussymmetrybreakingfromanyoncondensation |