  At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional
quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in
the isotropic FQH liquid. This correspondence would be exact as the GMP mode
softens upon approach to the putative point of a quantum phase transition to a
FQH nematic. Motivated by these considerations as well as by suggestive
evidence of an FQH nematic in tilted field experiments, we have sought evidence
of such a nematic FQHE in a microscopic model of interacting electrons in the
lowest Landau level at filling factor 1/3. Using a family of anisotropic
Laughlin states as trial wave functions, we find a continuous quantum phase
transition between the isotropic Laughlin liquid and the FQH nematic. Results
of numerical exact diagonalization also suggest that rotational symmetry is
spontaneously broken, and that the phase diagram of the model contains both a
nematic and a stripe phase.
