Trial Wavefunctions for the Goldstone Mode in Quantum Hall Bilayers
Figure 1
Overlaps of the trial states (3) with the exact eigenstates of the Coulomb Hamiltonian for a selection of system sizes , 12, 14, and 16 on the sphere. The magnitude of the overlap of the trial state with the exact ground state is indicated by the size of red dark shaded circles. Blue lightly shaded circles additionally indicate the overlap of the same trial states with the first excited state of the exact spectrum. Overlaps at are equal to one by definition and give the overall scale. The trial states are very accurate at , giving a good description of the lowest energy mode in each sector of angular momentum (the Goldstone mode) up to large . At finite layer separation , the Goldstone mode is always present at small but does not reach to similarly high values of angular momentum. The description is again more successful at very large .
