CaltechAUTHORS
  A Caltech Library Service

Loops in 4+1d Topological Phases

Chen, Xie and Dua, Arpit and Hsin, Po-Shen and Jian, Chao-Ming and Shirley, Wilbur and Xu, Cenke (2021) Loops in 4+1d Topological Phases. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220113-234540268

[img] PDF - Submitted Version
See Usage Policy.

2MB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20220113-234540268

Abstract

2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form ℤ₂ gauge field (the loop only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self `exchange' statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2,ℤ₂) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the 'fractional Maxwell theory' and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the ℤ₂ gauge group to ℤ_N.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2112.02137arXivDiscussion Paper
ORCID:
AuthorORCID
Hsin, Po-Shen0000-0002-4764-1476
Additional Information:We would like to thank Fiona Burnell, Meng Cheng, Lukasz Fidkowski, Jeongwan Haah, Yi Ni, Xiao-Liang Qi, Nathan Seiberg, Shu-Heng Shao, Kevin Walker and Zhenghan Wang for valuable discussions. A.D. thanks Yu-An Chen for the useful discussion on higher cup products. W.S., A.D., and X.C. were supported by the Simons Foundation through the collaboration on Ultra-Quantum Matter (651438, XC), the Walter Burke Institute of Theoretical Physics, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907), the National Science Foundation (DMR-1654340, XC) and the Simons Investigator Award (828078, XC). W.S. is also supported by a grant from the Simons Foundation (651444, WS). The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, by the Simons Foundation through the Simons Investigator Award, and by the Simons Collaboration on Global Categorical Symmetries. C. X. is supported by NSF Grant No. DMR-1920434 and the Simons Investigator program.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Simons Foundation651438
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
NSFDMR-1654340
Simons Foundation828078
Simons Foundation651444
Department of Energy (DOE)DE-SC0011632
NSFDMR-1920434
Record Number:CaltechAUTHORS:20220113-234540268
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220113-234540268
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112898
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Jan 2022 15:53
Last Modified:14 Jan 2022 15:53

Repository Staff Only: item control page