Trial wave functions for a Composite Fermi liquid on a torus

Abstract

We study the two-dimensional electron gas in a magnetic field at filling fraction $\nu =\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

arXiv comment16 pages, 12 figures v2. Added a figure, and corrected scale on some figures

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Cited by in corpus (18)

• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Berry phase and model wavefunction in the half-filled Landau Level
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Bootstrapping the Quantum Hall problem
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Self-similarity of spectral response functions for fractional quantum Hall states
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• On the modular covariance properties of composite fermions on the torus
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions