The fractionally charged quasiparticle states are constructed to describe the elementary excitations of double-layer quantum Hall systems. It is shown that the quasiparticle states not only predict correctly the parities of the low-lying energy states as the system away from filling factor 2/(m+n) by adding or removing one flux quantum, but also have fairly large overlaps with them. Right at ν=2/(m+n), we propose quasiexciton (a pair of a positively charged quasiparticle and a negatively charged quasiparticle) states, which have two branches with parities opposite in sign, to describe the collective excitations of the system. The validity of the quasiexciton states, as well as the recently proposed density wave states, is studied. To characterize the peculiar order of the double-layer quantum Hall ground state, we show that Halperin’s (mmn) state possesses an off-diagonal long-range order (ODLRO) due to the coherence between (mmn) states with different numbers of electrons. We study the ODLRO of the ground states of a finite system at various layer separations. We find that in a wide range of layer separations the ground state, which has a finite overlap with the (mmn) state, always exhibits the ODLRO, in contrast to what we observe in the case by lowering the short-range pseudopotential, where the ODLRO is suddenly lost at a critical value, accompanied by a vanishing overlap between the ground state and the (mmn) state.

• Received 19 December 1994

DOI:https://doi.org/10.1103/PhysRevB.51.16954