Codimension-2 defects and higher symmetries in (3+1)D topological phases
Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu
SciPost Phys. 14, 065 (2023) · published 11 April 2023
- doi: 10.21468/SciPostPhys.14.4.065
- Submissions/Reports
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 $\mathbb{Z}_2$ gauge theory with fermionic charges, in $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ($D_n$) and alternating ($A_6$) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an $H^4$ 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 $A_6$ gauge theory.
Cited by 11
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Maissam Barkeshli,
- 1 2 Yu-An Chen,
- 1 Sheng-Jie Huang,
- 1 Ryohei Kobayashi,
- 3 4 Nathanan Tantivasadakarn,
- 5 Guanyu Zhu
- 1 Joint Quantum Institute
- 2 University of Maryland, College Park [UMCP]
- 3 Harvard University
- 4 Walter Burke Institute for Theoretical Physics
- 5 IBM Quantum