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Title: Codimension-2 defects and higher symmetries in (3+1)D topological phases

Abstract

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.

Authors:
 [1];  [2];  [1];  [1];  [3];  [4]
+ Show Author Affiliations
  1. Joint Quantum Institute
  2. Joint Quantum Institute, University of Maryland, College Park
  3. Harvard University, Walter Burke Institute for Theoretical Physics
  4. IBM Quantum
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1969419
Grant/Contract Number:  
SC0012704
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 14 Journal Issue: 4; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Barkeshli, Maissam, Chen, Yu-An, Huang, Sheng-Jie, Kobayashi, Ryohei, Tantivasadakarn, Nathanan, and Zhu, Guanyu. Codimension-2 defects and higher symmetries in (3+1)D topological phases. Netherlands: N. p., 2023. Web. doi:10.21468/SciPostPhys.14.4.065.
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Barkeshli, Maissam, Chen, Yu-An, Huang, Sheng-Jie, Kobayashi, Ryohei, Tantivasadakarn, Nathanan, & Zhu, Guanyu. Codimension-2 defects and higher symmetries in (3+1)D topological phases. Netherlands. https://doi.org/10.21468/SciPostPhys.14.4.065
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Barkeshli, Maissam, Chen, Yu-An, Huang, Sheng-Jie, Kobayashi, Ryohei, Tantivasadakarn, Nathanan, and Zhu, Guanyu. Tue . "Codimension-2 defects and higher symmetries in (3+1)D topological phases". Netherlands. https://doi.org/10.21468/SciPostPhys.14.4.065.
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@article{osti_1969419,
title = {Codimension-2 defects and higher symmetries in (3+1)D topological phases},
author = {Barkeshli, Maissam and Chen, Yu-An and Huang, Sheng-Jie and Kobayashi, Ryohei and Tantivasadakarn, Nathanan and Zhu, Guanyu},
abstractNote = {(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.},
doi = {10.21468/SciPostPhys.14.4.065},
journal = {SciPost Physics},
number = 4,
volume = 14,
place = {Netherlands},
year = {Tue Apr 11 00:00:00 EDT 2023},
month = {Tue Apr 11 00:00:00 EDT 2023}
}
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