Predictive states and predictive complexity of subsystems of the one-dimensional Heisenberg model

We define predictive states and predictive complexity for subsystems of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy or local magnetization, the predictive complexity better signifies dynamically important events, such as magnon collisions. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory, but is intrinsically quantum, and can serve as a local order parameter that can distinguish long and short range entanglement.