Microscopic theory for the nematic fractional quantum Hall effect

We analyse properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary microscopic conditions for the FQHN to be robust. Analytical expressions of the degenerate ground state manifold and gapless nematic modes are given in compact forms with the input interaction and the ground state structure factors. We relate the long wavelength limit of the neutral excitations (serving as the FQHN ground state from spontaneous symmetry breaking) to the guiding center metric deformation, and show explicitly the family of trial wavefunctions for the nematic modes with spatially varying nematic order. For short range interactions, the dynamics of the FQHN is determined by the long wavelength part of the ground state structure factor, leading to potentially more efficient numerical approaches. The special case of the FQHN at ν = 1/3 is discussed with theoretical insights from the Haffnian parent Hamiltonian, leading to a number of rigorous statements and experimental implications. This allows us to discuss the possibility of the linear Goldstone modes proposed in the effective theory from the microscopic perspective. (PR RESEARCH 2, 033362 (2020))