DELOCALIZATION TRANSITION VIA SUPERSYMMETRY IN ONE-DIMENSION

We use supersymmetric (SUSY) methods to study the delocalization trans ition at zero energy in a one-dimensional tight-binding model of spinl ess fermions with particle-hole symmetric disorder. Like the McCoy-Wu random transverse-field Ising model to which it is related, the fermio nic problem displays two different correlation lengths for typical and mean correlations. Using the SUSY technique, mean correlators are obt ained as quantum-mechanical expectation values for a U(2/1, 1) ''super spin.'' In the scaling limit, this quantum mechanics is closely relate d to a 0 + 1-dimensional Liouville theory, allowing an interpretation of the results in terms of simple properties of the zero-energy wave f unctions. Our primary results are the exact two-parameter scaling func tions for the mean single-particle Green's functions. We also show how the Liouville quantum-mechanics approach can be extended to obtain th e full set of multifractal scaling exponents tau(q), y(q) at criticali ty. A thorough understanding of the unusual features of the present th eory may be useful in applying SUSY to other delocalization transition s.