Off-diagonal long-range order in the fractional quantum Hall effect

It is generally accepted that the fundamental physics of the fractional quantum Hall effect lies in the topological binding of quantized vortices and electrons. From a microscopic point of view, however, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study the Girvin-MacDonald off-diagonal long-range order at Landau level fillings $\nu=1/m$ ($m$ odd) for bosonic wave functions obtained from fermionic fractional Hall wave functions by a singular gauge transformation. In order to test the robustness of the concept, we work with accurate representations of the Coulomb ground state, constructed using the framework of the composite-fermion theory, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value $m/2$ independent of the form of the wave function. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.