Berry Phase and Model Wave Function in the Half-Filled Landau Level

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

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We construct model wave functions for the half-filled Landau level parametrized by "composite fermion occupation-number configurations" in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wave functions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.

Original languageEnglish (US)
Article number147202
JournalPhysical review letters
Volume121
Issue number14
DOIs
StatePublished - Oct 3 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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