Ground state, quasihole, a pair of quasihole wave functions, and instability in bilayer quantum Hall systems

The bilayer quantum Hall system (BLQH) differs from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudospin sector. Due to the gapless mode, qualitatively good ground-state and low energy excited-state wave functions at any finite distance are still unknown. We investigate this important open problem by the composite boson (CB) theory developed by one of the authors to study BLQH systematically. We derive the ground state, quasihole, and a pair of quasihole wave functions from the CB theory and its dual action. We find that the ground-state wave function is the product of two parts, one in the charge sector which is the well known Halperin (111) wave function and the other in the spin sector which is nontrivial at any finite d due to the gapless mode. So the total ground-state wave function differs from the well known (111) wave function at any finite d. In addition to commonly known multiplicative factors, the quasihole and a pair of quasihole wave functions also contain nontrivial normalization factors multiplying the correct ground state wave function. We expect that the quasihole and pair wave function not only has logarithmically divergent energy and well localized charge distribution, but also correct interlayer correlations. All the distance dependencies in all the wave functions are encoded in the spin part of the ground-state wave function. The instability encoded in the spin part of the ground-state wave function leads to the pseudo-spin-density wave proposed by one of the authors previously. Some subtleties related to the Lowest Landau Level (LLL) projection and shortcomings of the CB theory are also noted.