  The fractional quantum Hall (FQH) effect was discovered in two-dimensional
electron systems subject to a large perpendicular magnetic field nearly four
decades ago. It helped launch the field of topological phases, and in addition,
because of the quenching of the kinetic energy, gave new meaning to the phrase
"correlated matter". Most FQH phases are gapped like insulators and
superconductors; however, a small subset with even denominator fractional
fillings nu of the Landau level, typified by nu = 1/2, are found to be gapless,
with a Fermi surface akin to metals. We discuss our results, obtained
numerically using the infinite Density Matrix Renormalization Group (iDMRG)
scheme, on the effect of non-isotropic distortions with discrete N-fold
rotational symmetry of the Fermi surface at zero magnetic field on the Fermi
surface of the correlated nu = 1/2 state. We find that while the response for N
= 2 (elliptical) distortions is significant (and in agreement with experimental
observations with no adjustable parameters), it decreases very rapidly as N is
increased. Other anomalies, like resilience to breaking the Fermi surface into
disjoint pieces, are also found. This highlights the difference between Fermi
surfaces formed from the kinetic energy, and those formed of purely potential
energy terms in the Hamiltonian.
