Phase Diagram of strongly correlated one-dimensional fermions in   incommensurate potentials
  We study the interplay between strong correlations and incommensurability on fermions using mean field as well as exact many-body Lanczos diagonalization techniques. In a two-dimensional parameter space, mean field phase diagram of infinite system shows a critical phase with multifractal characteristics sandwiched between a Bloch-type extended and a localized phase. Exact numerical computation on finite size systems of the Kohn charge stiffness Dc, characterizing transport properties, and the charge exponent Krho, characterizing the superconducting pairing fluctuations, shows the existence of a phase with superconducting correlations. This phase may be characterized by a power law scaling of the charge stiffness constant in contrast to the Anderson localized phase where Dc scales exponentially with the size of the system. We argue that this intermediate phase may be a dressed up analog of the critical phase of the noninteracting fermions in an incommensurate potential. 
Juan Carlos Chaves, Indubala I. Satija and Mauro M. Doria