Trial Wavefunctions for the Goldstone Mode in Quantum Hall Bilayers
Figure 3
Spectra of the Coulomb Hamiltonian in the bilayer system on the sphere for particles with flux, for layer separations ranging from (top left) to (bottom right). Energies are indicated in units of relative to the ground state energy at . Red crosses mark the lowest two eigenstates in each sector of given . Blue circles indicate those states which were identified as part of the Goldstone branch by high overlaps (see Figure 1). At , the Goldstone mode is very well formed, while it is clearly visible at small and intermediate how there are level crossings with additional low lying excitations. At , a mode of low-lying excitations is once again clearly separated from the rest of the spectrum, which terminates sharply at . Its dispersion is linear at small , but it has a quadratic component responsible of the upturn at larger . Note the change in the scale of the -axis for the three columns of panels.
