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Symmetry-Enriched Quantum Spin Liquids in (3+1)d

Hsin, Po-Shen and Turzillo, Alex (2020) Symmetry-Enriched Quantum Spin Liquids in (3+1)d. Journal of High Energy Physics, 2020 (9). Art. No. 22. ISSN 1126-6708. doi:10.1007/JHEP09(2020)022.

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We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Hsin, Po-Shen0000-0002-4764-1476
Turzillo, Alex0000-0003-4293-4293
Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: April 1, 2020; Accepted: July 30, 2020; Published: September 2, 2020. We thank Zhen Bi, Xie Chen, Meng Cheng, Clay Córdova, Anton Kapustin, Hotat Lam, Kantaro Ohmori, Shu-Heng Shao, Ryan Thorngren and Juven Wang for discussions. The work was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of P.-S.H. was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Subject Keywords:Anomalies in Field and String Theories; Global Symmetries; Topological Field Theories; Topological States of Matter
Issue or Number:9
Record Number:CaltechAUTHORS:20190624-081116757
Persistent URL:
Official Citation:Hsin, P., Turzillo, A. Symmetry-enriched quantum spin liquids in (3 + 1)d. J. High Energ. Phys. 2020, 22 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96651
Deposited By: Tony Diaz
Deposited On:24 Jun 2019 17:10
Last Modified:16 Nov 2021 17:22

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