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APS » Journals » Phys. Rev. Lett. » Volume 103 » Issue 26
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Phys. Rev. Lett. 103, 261601 (2009) [4 pages]

Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure

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Steven T. Flammia1, Alioscia Hamma1, Taylor L. Hughes2,3, and Xiao-Gang Wen4,1
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5 Canada
2Department of Physics, Stanford University, Stanford, California 94305, USA
3Department of Physics, University of Illinois, Urbana-Champaign, Urbana, Illinois 61802, USA
4Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Received 17 September 2009; published 28 December 2009

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter α, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of α for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.103.261601
DOI:
10.1103/PhysRevLett.103.261601
PACS:
11.15.-q, 03.65.Ud, 71.10.-w, 11.25.-w
 
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