Glassy Relaxation and Breakdown of the Stokes-Einstein Rela- tion 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. The dynamics of supercooled liquids approaching the glass transition remains one of the most fundamental problems in condensed matter physics [1]. An important question concerning transport properties of supercooled liquids is the validity and possible breakdown of the Stokes-Einstein (SE) relation. There have been many experimental results [2] which show that highly supercooled liquids exhibit breakdown of the SE relation. Although there exist some theoretical attempts [3], the underlying microscopic mechanism for the violation of the SE relation is not well understood. In this work, by probing single particle and collective relaxation dynamics of the two dimensional (2D) lattice Coulomb gas (CG) with fractional charges parameterized by charge frustration f = p/q, we demonstrate that this non-random lattice model [4, 5] on a square lattice exhibits equilibrium relaxation behavior that closely resembles the primary relaxation of fragile supercooled liquids. Moreover, we observe that the model exhibits a strong violation of the SE relation at low temperatures, which is characterized by a fractional power law relation between the self-diffusion coefficient and the characteristic relaxation time. Recent molecular Typeset using EURO-TEX 2 EUROPHYSICS LETTERS dynamics simulations on the 2D [8, 9] and 3D binary liquids [10] also report the breakdown of the SE relation. General 2D CG on a square lattice is described by the following Hamiltonian that can be mapped from uniformly frustrated XY (UFXY) model by means of Villain transformation [11],