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

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.

References in corpus (3)

• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• A modular-invariant modified Weierstrass sigma-function as a building block for lowest-Landau-level wavefunctions on the torus
• Trial wave functions for a Composite Fermi liquid on a torus

Cited by in corpus (32)

• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Geometric Resonance of Four-Flux Composite Fermions
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Hall Viscosity of Composite Fermions
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Berry phase of the composite Fermi-liquid
• Electromagnetic response of composite Dirac fermions in the half-filled Landau level
• On the modular covariance properties of composite fermions on the torus
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Asymmetry of the Geometrical Resonances of Composite Fermions
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Fermi surfaces of composite fermions
• Fractional Quantum Hall States on CP2 Space
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Emergence of Dirac Composite Fermions: Dipole Picture