INTERACTING SPINLESS FERMIONS WITH DISORDER - THE MOTT TRANSITION FOR INFINITE COORDINATION-NUMBER

An analytic expression for the dynamical conductivity sigma (omega) of spinless fermions with local disorder and nearest-neighbour repulsion is derived on lattices with infinite coordination number Z. The model is exactly solvable in the whole parameter range assuming two possible phases: a homogeneous phase and a checkerboard charge-density wave (CDW). Away from half filling the system displays anomalous behaviour: weak particle-density fluctuations favour spontaneous symmetry breaking. First, we investigate the effects of this anomaly on the conductivity in the AC and DC regimes. Second, we focus on the Mott transition occurring at zero temperature at half filling. The critical exponents for the conductivity am computed for the dependence on the interaction U. the disorder gamma, the filling n, the temperature T and the frequency omega.