Counting edge modes via dynamics of boundary spin impurities

We study the dynamics of the one-dimensional Ising model in the presence of a static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find oscillatory correlations that decay as power laws. We uncover a phase diagram of dynamical responses where, upon tuning the strength of the boundary field, we observe distinct power laws that directly correspond to changes in the number of edge modes as the boundary and bulk magnetic field are varied. We suggest how the universal physics can be demonstrated in current experimental setups, such as Rydberg chains.