Fractional statistics and the butterfly effect

Fractional statistics and quantum chaos are both phenomena associated with the non-local storage of quantum information. in this article, we point out a connection between the butterfly effect in (1+1)-dimensional rational conformal field theories and fractional statistics in (2+1)-dimensional topologically ordered states. this connection comes from the characterization of the butterfly effect by the out-of-time-order-correlator proposed recently. we show that the late-time behavior of such correlators is determined by universal properties of the rational conformal field theory such as the modular s-matrix and conformal spins. using the bulk-boundary correspondence between rational conformal field theories and (2+1)-dimensional topologically ordered states, we show that the late time behavior of out-of-time-order-correlators is intrinsically connected with fractional statistics in the topological order. we also propose a quantitative measure of chaos in a rational conformal field theory, which turns out to be determined by the topological entanglement entropy of the corresponding topological order.