The fractional quantum Hall (FQH) nematic state is a conjectured state of matter in which FQH topological order coexists with spontaneously broken rotation symmetry. Recent experiments on GaAs quantum wells suggest this state, as well as the concomitant isotropic-nematic phase transition, may be realized in a two-dimensional electron gas at certain rational filling factors. Although effective field theories of the FQH nematic state have been constructed, there has been so far no explicit realization of this state as the ground state of a microscopic model of interacting electrons. The authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the FQH nematic state.
The authors study the dispersion of collective excitations for fractional quantum Hall states using Feynman-Bijl ansatz wavefunctions. They take the ground-state pair correlation function from direct diagonalisations of the Hamiltonian for a small number of electrons confined to the surface of a sphere, instead of from the simulation of large systems described by a Laughlin-like wavefunction. The results seem remarkably well converged considering the small systems used. They also treat systems with partially filled N=1 Landau levels.