Topological characterization of the non-Abelian Moore-Read state using density-matrix renormalization group

W. Zhu, S. S. Gong, F. D.M. Haldane, D. N. Sheng

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

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 density-matrix 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 ν=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.

Original languageEnglish (US)
Article number165106
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume92
Issue number16
DOIs
StatePublished - Oct 7 2015

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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