Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States
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PhysRevLett.115.036802.pdf
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223.24 KB
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Author(s)
Moradi, Heidar
Wen, Xiao-Gang
Date Issued
July 2015
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Moradi, Heidar, and Xiao-Gang Wen. "Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States." Phys. Rev. Lett. 115, 036802 (July 2015). Copyright © 2015 American Physical Society
Version
Final published version
Abstract
We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M[superscript d]) of closed spatial manifold M[superscript d]. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.115.036802
