Microscopic theory for nematic fractional quantum Hall effect

Abstract

We analyse various microscopic properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust. Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic 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 to the guiding center metric deformation, and show explicitly the family of trial wavefunctions for the nematic modes with spatially varying nematic order near the quantum critical point. For short range interactions, the dynamics of the FQHN is completely determined by the long wavelength part of the ground state structure factor. The special case of the FQHN at $\nu=1/3$ is discussed with new theoretical insights from the Haffnian parent Hamiltonian, leading to a number of rigorous statements and experimental implications.