Glassy Relaxation and Breakdown of the Stokes-Einstein Relation in the Two Dimensional Lattice Coulomb Gas of Fractional Charges

We present Monte Carlo simulation results on the equilibrium relaxation of the two dimensional lattice Coulomb gas with fractional charges, which exhibits a close analogy to the primary relaxation of fragile supercooled liquids. Single particle and collective relaxation dynamics show that the Stokes-Einstein relation is violated at low temperatures, which can be characterized by a fractional power law relation between the self-diffusion coefficient and the characteristic relaxation time. The microscopic spatially heterogeneous structure responsible for the violation is identified.