Universality of the Edge Tunneling Exponent of Fractional Quantum Hall Liquids

In a microscopic model of fractional quantum Hall liquids with electron-electron interactions and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu=1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent. In particular, for $\nu=1/3$ with Coulomb interactions and a hard edge, the tunneling exponent is non-universal as found previously. However, the universal value is recovered if the hard-edge confinement is relaxed or a neutralizing background charge is placed a distance $d < d_c$ from the 2-D layer. At the critical distance $d_c$ the edge reconstructs and we find two distinct power law regimes over two different length scales. On the longer length scale the system recovers its universal exponent.