Revealing Topological Features via Dynamics: a Parametrically Modulated Spin Chain

Nontrivial topology leads to a change in the system dynamics compared to topologically trivial systems. We study such a change for a parametrically modulated spin chain in a strong magnetic field. The system maps onto Kitaev’s chain with tunable parameters of fermion pairing and chemical potential, which are determined by the modulation amplitude and frequency, respectively. The modulation frequency thus determines whether the system is in the topologically nontrivial regime. For a periodic chain, we obtain explicit solutions for the evolution of the system for the modulation parameters varying sharply and slowly. We show that the spin correlation functions are qualitatively different in the trivial and topological regimes and find the scaling of the region of nonadiabatic behavior with the increasing modulation amplitude near the phase transition and in the nontrivial regime. We also find that varying the modulation frequency to enter the topological regime produces a different response than when the modulation is switched on with its frequency already in the topological regime, indicating a hysteresis-like effect. For an open chain, we show how the system of Kitaev’s fermions responds to turning on the modulation for different modulation frequencies and how a surface state is split off the band of extended fermionic states on entering the nontrivial regime. We analyze how the surface states are excited and how they affect spin correlations.