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Moradi H, Wen XG. Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States. Phys Rev Lett. 2015;115(3):036802doi: 10.1103/PhysRevLett.115.036802.
Moradi, H., & Wen, X. G. (2015). Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States. Physical review letters, 115(3), 036802. https://doi.org/10.1103/PhysRevLett.115.036802
Moradi, Heidar, and Wen, Xiao-Gang. "Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States." Physical review letters vol. 115,3 (2015): 036802. doi: https://doi.org/10.1103/PhysRevLett.115.036802
Moradi H, Wen XG. Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States. Phys Rev Lett. 2015 Jul 17;115(3):036802. doi: 10.1103/PhysRevLett.115.036802. Epub 2015 Jul 14. PMID: 26230815.
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Phys Rev Lett. 2015 Jul 17;115(3):036802. doi: 10.1103/PhysRevLett.115.036802. Epub 2015 Jul 14.

Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States.

Physical review letters

Heidar Moradi, Xiao-Gang Wen

Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

PMID: 26230815 DOI: 10.1103/PhysRevLett.115.036802

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^{d}) of closed spatial manifold M^{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.

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