Off-diagonal long range order in disordered quantum Hall systems

Gun Sang Jeon, Michael Ronald Peterson, Jainendra K. Jain

Shivaji L. Sondhi, Martin P. Gelfand

We have numerically studied bosonic off-diagonal long range order, introduced by Read to describe the ordering in ideal quantum Hall states, for noninteracting electrons in random potentials confined to the lowest Landau level. We find that it also describes the ordering in disordered quantum Hall states; the proposed order parameter vanishes in the disordered (${\ensuremath{\sigma}}_{\mathrm{xy}}=0$) phase and increases continuously from zero in the ordered (${\ensuremath{\sigma}}_{\mathrm{xy}}=\frac{{e}^{2}}{h}$) phase. We study the scaling of the order parameter and find that it is consistent with that of the one-electron Green function.

Wade DeGottardi, Mohammad Hafezi

Edward H. Rezayi, F. D. M. Haldane

We present evidence of off-diagonal long-range order in the incompressible fractional quantum Hall states at $\ensuremath{\nu}=\frac{1}{3} \mathrm{and} \frac{2}{5}$ Landau-level fillings. We construct correlation functions that exhibit this property only for incompressible quantum-Hall-effect states. In a compressible state no off-diagonal long-range order is observed.

Gang Su

Xin Xie, Song He, S. Das Sarma

A new nonsingular mapping between bosons and fermions is introduced in connection with the fractional quantum Hall effect. The mapping connects a fermion system of filling ${\ensuremath{\nu}}_{\mathit{f}}$ to a boson system of filling ${\ensuremath{\nu}}_{\mathit{b}}$ through the relation ${\ensuremath{\nu}}_{\mathit{f}}^{\mathrm{\ensuremath{-}}1}$=${\ensuremath{\nu}}_{\mathit{b}}^{\mathrm{\ensuremath{-}}1}$+1. The ground state of the boson system is shown to map accurately to that of the fermion system if and only if they are both incompressible quantum Hall states. The accuracy of the mapping is shown to be related to the validity of the mean-field theory. The relevance of this mapping to off-diagonal long-range order is discussed by numerically studying the binding of wave-function zeros to particle positions.