Berry phase and model wavefunction in the half-filled Landau Level

TL;DR

This paper constructs model wavefunctions for the half-filled Landau level, formulates a many-body Berry phase for quasiparticle transport, and finds a universal phase of π, advancing understanding of composite fermions in quantum Hall systems.

Contribution

It introduces a many-body Berry phase framework for composite fermions and connects it with exact eigenstates, providing new insights into quasiparticle transport in the half-filled Landau level.

Findings

Wavefunctions with high overlap to exact states are constructed.

A many-body Berry phase of exactly π is computed for quasiparticle transport.

The Berry phase is related to a density operator and momentum boost matrix elements.

Abstract

We construct model wavefunctions for the half-filled Landau level parameterized 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 large overlap with wavefunctions obtained by 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 wavefunctions" 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 computation of the Berry phase for 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 $\pi$ for this process.