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Twisted gauge theories in three-dimensional Walker-Wang models

Wang, Zitao and Chen, Xie (2017) Twisted gauge theories in three-dimensional Walker-Wang models. Physical Review B, 95 (11). Art. No. 115142. ISSN 2469-9950. doi:10.1103/PhysRevB.95.115142.

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Three-dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be “twisted,” in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized in models discovered by Dijkgraaf and Witten. A different framework to systematically construct three-dimensional topological phases was proposed by Walker and Wang and a series of examples have been studied. Can the Walker-Wang construction be used to realize the topological order in twisted gauge theories? This is not immediately clear because the Walker-Wang construction is based on a loop condensation picture while the Dijkgraaf-Witten theory is based on a membrane condensation picture. In this paper, we show that the answer to this question is Yes, by presenting an explicit construction of the Walker-Wang models which realize both the twisted and untwisted gauge theories with gauge group Z_2×Z_2. We identify the topological order of the models by performing modular transformations on the ground-state wave functions and show that the modular matrices exactly match those for the Z_2×Z_2 gauge theories. By relating the Walker-Wang construction to the Dijkgraaf-Witten construction, our result opens up a way to study twisted gauge theories with fermonic charges, and correspondingly strongly interacting fermionic symmetry protected topological phases and their surface states, through exactly solvable models.

Item Type:Article
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URLURL TypeDescription Paper
Wang, Zitao0000-0002-2326-2674
Alternate Title:Twisted gauge theories in 3D Walker-Wang models
Additional Information:© 2017 American Physical Society. Received 15 January 2017; published 24 March 2017. We would like to thank Meng Cheng, Lukasz Fidkowski, Yuting Hu, and Zhenghan Wang for valuable discussions, and especially Yichen Huang for discussions and collaborations during various stages of the work. X.C. is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Issue or Number:11
Record Number:CaltechAUTHORS:20170206-091125776
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Official Citation:Twisted gauge theories in three-dimensional Walker-Wang models Zitao Wang and Xie Chen Phys. Rev. B 95, 115142
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74068
Deposited By: Ruth Sustaita
Deposited On:06 Feb 2017 17:26
Last Modified:11 Nov 2021 05:24

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