Competition of random and periodic potentials in interacting fermionic systems and classical equivalents: the Mott Glass

We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one dimensional interacting fermionic systems but higher dimensional bosonic and fermionic extensions, as well as classical equivalents are also discussed. Our methods which include bosonization, replica variational method, functional renormalization group (RG) and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson Insulator (compressible, with a pseudogap in the optical conductivity) and the Mott Insulator (incompressible with a gap in the optical conductivity). The Mott glass, which was unexpected from a perturbative renormalization group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of the Mott Glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimension. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.