Journal
PHYSICAL REVIEW B
Volume 92, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.92.165106
Keywords
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Funding
- U.S. Department of Energy, Office of Basic Energy Sciences [DE-FG02-06ER46305]
- National Science Foundation [DMR-1408560, DMR-1205734]
- Princeton MRSEC Grant [DMR-1420541]
- W. M. Keck Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1408560, 1205734] Funding Source: National Science Foundation
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The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on a densitymatrix renormalization-group calculation, we provide a complete characterization of the universal properties of the bosonic Moore-Read state on a Haldane honeycomb lattice model at filling number nu = 1 for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through simulating a flux-inserting experiment, it is found that two of the Abelian ground states can be adiabatically connected, whereas the ground state in the Ising anyon sector evolves back to itself, which reveals the fusion rules between different QPs in real space. Furthermore, we calculate the modular matrices S and u, which contain all the information for the anyonic QPs, such as quantum dimensions, fusion rule, and topological spins.
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