Title: Nematic order in fractional quantum Hall liquids

Abstract:

The fractional quantum Hall (FQH) nematic is a conjectured state of matter in which a fractional quantized Hall conductivity coexists with the spontaneous breaking of rotational symmetry characteristic of a nematic liquid crystal. Although effective field theories and model wave functions for this state have been constructed, no direct evidence for its occurrence in a microscopic model of interacting electrons has been found so far. We find such evidence by using exact numerical diagonalization to study a model of interacting electrons confined to a two-dimensional plane in a perpendicular magnetic field. Upon varying a single coupling constant we find a quantum phase transition signaled by the simultaneous closing of the energy gap of the Girvin-MacDonald-Platzman collective mode in the isotropic FQH liquid, and the occurrence of a maximum in a suitably defined nematic susceptibility. Exact diagonalization results are found to compare favorably with the predictions of field-theoretic and variational descriptions of an FQH isotropic-to-nematic transition. Implications for recent experiments are discussed.