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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Many-Body Physics

Background:

  • The study of half-filled Landau levels is crucial for understanding emergent phenomena in two-dimensional electron systems.
  • Composite fermions are key quasiparticles in explaining the fractional quantum Hall effect.
  • Exact diagonalization and model wave functions are standard tools for theoretical investigations.

Purpose of the Study:

  • To construct model wave functions for half-filled Landau levels using composite fermion configurations.
  • To formulate and evaluate a many-body Berry phase for composite fermion transport.
  • To identify exact eigenstates with quasiparticle configurations.

Main Methods:

  • Construction of model wave functions parametrized by composite fermion occupation-number configurations.
  • Exact diagonalization of lowest-Landau-level electrons with Coulomb interaction.
  • Formulation of a many-body Berry phase using adiabatic transport of single quasiparticles.
  • Reinterpretation of Bloch wave function overlaps using momentum boost and density operators.

Main Results:

  • Model wave functions show large overlap with exact diagonalization states for weakly excited Fermi seas.
  • A many-body Berry phase for composite fermion transport around the Fermi surface is computed.
  • A phase contribution from the density operator and an additional phase of exactly π are identified.

Conclusions:

  • The developed model wave functions provide a link between exact states and quasiparticle configurations.
  • The many-body Berry phase formulation offers a new perspective on quasiparticle dynamics.
  • The finding of a π phase is significant for understanding topological properties in quantum Hall systems.