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Identifying Non-Abelian Topological Order through Minimal Entangled States

Author(s): Zhu, W; Gong, SS; Haldane, Frederick D; Sheng, DN

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Abstract: The topological order is encoded in the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order for topological band models through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice models with bosonic particles. We identify multiple independent minimal entangled states (MESs) in the ground state manifold on a torus. The extracted modular S matrix from MESs faithfully demonstrates the Ising anyon or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings unambiguously demonstrate the topological nature of the quantum states for these flatband models without using the knowledge of model wave functions.
Publication Date: 7-Mar-2014
Electronic Publication Date: 4-Mar-2014
Citation: Zhu, W, Gong, SS, Haldane, FDM, Sheng, DN. (2014). Identifying Non-Abelian Topological Order through Minimal Entangled States. PHYSICAL REVIEW LETTERS, 112 (10.1103/PhysRevLett.112.096803
DOI: doi:10.1103/PhysRevLett.112.096803
ISSN: 0031-9007
EISSN: 1079-7114
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW LETTERS
Version: Final published version. This is an open access article.



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