Microscopic theory for the nematic fractional quantum Hall effect

We analyse various properties of the nematic fractional quantum Hall effect (FQHE) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust. Analytical expressions of the degenerate ground state manifold, ground state energies, and gapless Goldstone modes are given in compact forms with the input interaction and the corresponding ground state structure factors. We relate the long wavelength limit of the neutral excitations (serving as the nematic FQHE ground state from spontaneous symmetry breaking) to the guiding center metric deformation, and show explicitly the family of trial wavefunctions for the Goldstone modes with spatially varying nematic order. We show for short range interactions, the dynamics of the nematic FQH is completely determined by the long wavelength part of the ground state structure factor. This is the only part that requires numerical studies in the future work, which is potentially more tractable than the conventional numerical approaches.