Minimal entangled states and modular matrix for fractional quantum Hall effect in topological flat bands

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

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low-energy states. We identify multiple independent minimal entangled states, which form a set of orthogonal basis states for the ground-state manifold. We extract the modular transformation matrices S (U) which contain the information of mutual (self) statistics, quantum dimensions, and the fusion rule of quasiparticles. Moreover, we demonstrate that these matrices are robust and universal in the whole topological phase against different perturbations until the quantum phase transition takes place.

Original languageEnglish (US)
Article number035122
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume88
Issue number3
DOIs
StatePublished - Jul 17 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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