Infinite density matrix renormalization group for multicomponent quantum Hall systems

Michael P. Zaletel, Roger S.K. Mong, Frank Pollmann, Edward H. Rezayi

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


While the simplest quantum Hall plateaus, such as the ν=1/3 state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher-Landau-level indices play an important role. These "multicomponent" problems are difficult to study using exact diagonalization because each component increases the difficulty exponentially. An important example is the plateau at ν=5/2, where scattering into higher Landau levels chooses between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address the methodological issues required to apply the infinite density matrix renormalization group to quantum Hall systems with multiple components and long-range Coulomb interactions, greatly extending accessible system sizes. As an initial application we study the problem of Landau-level mixing in the ν=5/2 state. Within the approach to Landau-level mixing used here, we find that at the Coulomb point the anti-Pfaffian state is preferred over the Pfaffian state over a range of Landau-level mixing up to the experimentally relevant values.

Original languageEnglish (US)
Article number045115
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number4
StatePublished - Jan 14 2015

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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