The single-mode description of the integer quantum Hall state with dipole-dipole interaction

A topological phase can often be represented by a corresponding wavefunction (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wavefunction fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We demonstrate the recovery of the variational parameter in a single-mode approximation, which is consistent with the recently proposed geometric consideration of the quantum Hall phases.