A model wavefunction for the composite Fermi liquid: its geometry and entanglement.

I will describe a model wavefunction for the composite Fermi liquid in a partially-filled Landau level, recently formulated in a torus geometry (Shao et al., Phys. Rev. Lett. 114, 206402 (2015)), that allows a manifold of gapless composite Fermi-liquid states to be characterized, parametrized by an analog of the ``occupation number'' that defines the Fermi surface in a free-electron gas. Unlike incompressible FQHE states, which only occur in an inversion-symmetric momentum sector, these CFL states occur in each distinct momentum sector allowed by the periodic boundary condition. The fundamental wavefunction of this type describes a system with $\nu$ = 1/2, but multiplication by (or division by) a Vandermonde factor describes states at $\nu$ = $1/m$. The CFL states are characterized by an ``intrinsic metric" which determines the shape of the Fermi surface, and corresponds to the shape of the ``flux-attachment'' that forms the composite fermion. The wavefunction is well-suited for Monte-Carlo calculations, as it is analogous to a determinant form used by Jain in spherical geometry. The violation of ``area-law" (perimeter-law) entanglement found in Monte-Carlo calculations will be described.