Nature of the long-range order in the quantum Hall effect regime

We have studied the off-diagonal long-range order in the Laughlin state under a singular gauge transformation by studying the one-body density matrix in an equivalent classical plasma system within the hypernetted-chain and Monte Carlo schemes. The results for the one-body density matrix obtained by various plasma models agree with very accurate Monte Carlo results. In the quantum Hall regime, we find at most the power-law decay of the one-body density matrix for any Landau-level filling.