Microscopic tests of topological electron-vortex binding in the fractional Hall effect

The topological binding of quantized vortices and electrons plays a crucial role in our understanding of the fractional quantum Hall effect, and is manifest in the prototypical wave functions for the fractional Hall states. However, from a microscopic point of view, the non-Pauli vortices are not strictly bound to electrons in realistic ground state wave functions. We study here the Girvin-MacDonald off-diagonal long-range order for certain bosonic wave functions at Landau level fillings ν=1∕m (m odd), obtained from fermionic fractional Hall wave functions by a singular gauge transformation, and find strong evidence that the exponent describing its long-distance algebraic decay has a universal value equal to m∕2. We interpret this to mean that the topological notion of electron-vortex binding remains generally well defined as a long-distance property.