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Topological phases with generalized global symmetries

Yoshida, Beni (2016) Topological phases with generalized global symmetries. Physical Review B, 93 (15). Art. No. 155131. ISSN 1098-0121. doi:10.1103/PhysRevB.93.155131.

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We present simple lattice realizations of symmetry-protected topological phases with q-form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d+1)-colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.

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Additional Information:© 2016 American Physical Society. Received 2 September 2015; revised manuscript received 5 February 2016; published 15 April 2016. I would like to thank Z. Gu, A. Kubica, J. Preskill, B. Şahinoğlu, R. Thorngren, M. Walter, and D. Williamson for helpful discussions, conversations, and/or comments. Part of the work was completed during the visit to the Kavli Institute for Theoretical Physics. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants No. PHY-0803371 and No. PHY-1125565). I was supported by a David and Ellen Lee Postdoctoral Fellowship. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter
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Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Ellen Lee Postdoctoral FellowshipUNSPECIFIED
Issue or Number:15
Record Number:CaltechAUTHORS:20151005-094731380
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Official Citation:Topological phases with generalized global symmetries Beni Yoshida Phys. Rev. B 93, 155131
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60754
Deposited By: Tony Diaz
Deposited On:05 Oct 2015 18:13
Last Modified:10 Nov 2021 22:38

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