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Numerical detection of symmetry-enriched topological phases with space-group symmetry

Wang, Ling and Essin, Andrew and Hermele, Michael and Motrunich, Olexei (2015) Numerical detection of symmetry-enriched topological phases with space-group symmetry. Physical Review B, 91 (12). Art. No. 121103. ISSN 1098-0121. doi:10.1103/PhysRevB.91.121103.

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Topologically ordered phases of matter, in particular so-called symmetry-enriched topological phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone. We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state; we study the minima of the spectrum of correlation lengths of the transfer matrix for a cylinder. As a benchmark, we demonstrate our method using a modified toric code model with perturbation. An enhanced periodicity in momentum clearly reveals the nontrivial anticommutation relation {T_x, T_y}=0 for the corresponding quasiparticles in the system.

Item Type:Article
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URLURL TypeDescription DOIArticle Paper
Motrunich, Olexei0000-0001-8031-0022
Additional Information:© 2015 American Physical Society. Received 9 September 2014; published 4 March 2015. We would like to thank F. Verstraete and R. Mong for useful discussion. This work was supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250, by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-FG02-10ER46686 (M.H.), by Simons Foundation Grant No. 305008 (M.H. sabbatical support), and by the National Science Foundation through Grant No. DMR-1206096 (O.M.).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Department of Energy (DOE)DE-FG02-10ER46686
Simons Foundation305008
Issue or Number:12
Classification Code:PACS: 05.30.Pr, 71.15.Qe, 75.10.Jm, 75.10.Kt
Record Number:CaltechAUTHORS:20150410-083507920
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56566
Deposited By: Tony Diaz
Deposited On:10 Apr 2015 15:59
Last Modified:10 Nov 2021 21:00

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