Fractional charge and correlation exponents for interacting electrons in one dimension

Close to the transition between incommensurate conductor and commensurate insulator, charge transport in a system of one-dimensional interacting spin-1/2 fermions moving in a periodic potential is done by solitons (i.e., the few extra particles or holes) having a charge Q which is a fraction of the elementary charge e. We show that Q is directly related to the limiting value at commensuration of the exponent gc* of the charge-charge correlation function: gc*=(Q/e)2. We give some simple rules for determining both charge and spin correlation exponents and point out their dependence on the parity of the order of the underlying umklapp scattering.