Lattice Monte Carlo for quantum Hall states on a torus

Jie Wang, Scott D. Geraedts, E. H. Rezayi, F. D.M. Haldane

Research output: Contribution to journalArticle

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Abstract

The Monte Carlo method is very useful for studying various model states proposed for the fractional quantum Hall systems. In this paper, we introduce a lattice Monte Carlo method based on an exact lattice formalism for quantum Hall problems defined on a torus. This "lattice representation" is applied to study the many body Berry phase of the composite-Fermi liquid phase in a half-filled Landau level. The Monte Carlo result agrees with the exact numerical result found on small systems sizes and is consistent with the prediction from the Dirac fermion low-energy effective theory. Many other aspects of other model states, including the structure factor, Coulomb energy and particle-hole symmetry, are studied and discussed.

Original languageEnglish (US)
Article number125123
JournalPhysical Review B
Volume99
Issue number12
DOIs
StatePublished - Mar 15 2019

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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