Berry Phase in Composite-Fermi-Liquid States

The Composite-Fermi-Liquid (CFL) state is a gapless state that can occur at Landau-level filling 1/m when m is even, and an emergent Fermi surface for composite fermions forms. We examine the Berry phase associated with moving one composite fermion around different closed paths near the Fermi surface, using a model wavefunction parameterized by “composite-fermion occupation patterns” that explicitly has a Fermi surface. When these patterns correspond to weakly excited Fermi Sea, they are very accurate approximation for the exact Coulomb-interaction ground states, allowing exact states to be identified with composite-fermion configurations. A many-body analog of the k-space Berry phase is defined and examined both from exact states by exact diagonization and from comparison with model wavefunctions by the recently proposed lattice Monte Carlo method [arXiv: 1710.09729]. We also comment on the origin of the Dirac cone, and the one-quarter-filled state which is not particle-hole symmetric.