Berry Phase and Model Wave Function in the Half-Filled Landau Level.
Scott D Geraedts1,2, Jie Wang1, E H Rezayi3
1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|October 20, 2018
Summary
We developed a new method to study composite fermions in quantum systems. This research reveals a key phase of π during quasiparticle transport, advancing our understanding of fractional quantum Hall effects.
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.
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