Fractional diffusion without disorder in two dimensions

We analyze how simple local constraints in two dimensions lead a defect to exhibit robust, nontransient, and tunable subdiffusion. We uncover a rich dynamical phenomenology realized in ice- and dimer-type models. On the microscopic scale, a single defect exhibits anomalously long retractions. Such retractions result in a form of dynamical caging and can be captured through an effective fractional diffusion equation. Mapping to a height field yields an effective random walk subject to an emergent (entropic) logarithmic potential, whose strength is tunable, related to the exponent of algebraic ground-state correlations. The defect's path, viewed as nonequilibrium growth process, yields a frontier of fractal dimension of 5 / 4 , the value for a loop-erased random walk, rather than 4 / 3 for simple and self-avoiding random walks. Such frustration/constraint-induced subdiffusion is expected to be relevant to platforms, such as artificial spin ice and quantum simulators aiming to realize discrete link models and emergent gauge theories.