Projective construction of the Zk Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Cécile Repellin, Titus Neupert, B. Andrei Bernevig, Nicolas Regnault

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the Zk Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of Zk ground states on the torus. We develop an alternative projective construction of Zk Read-Rezayi states that complements the existing one. On the multilayer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend our symmetrization scheme to the plane and sphere geometries.

Original languageEnglish (US)
Article number115128
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume92
Issue number11
DOIs
StatePublished - Sep 14 2015

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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