Magnetization oscillations in a periodically driven transverse field Ising chain

The nonequilibrium dynamics of the magnetization in an Ising chain subjected to a slowly rotating transverse field is investigated, where we found the magnetization oscillations can be explained by the contributions from different particle excitations in the quantum E8 integrable model. We then further study the magnetization in the frequency domain in detail, uncovering a series of singular peaks for the z (Ising) component. These singular peaks are split into two sets for the magnetization along x and y directions with frequency shifts set by the rotational-field frequency. The peaks include both δ-function type and edge-singularity type peaks. The δ-function peaks can be attributed to particle excitations involving an E8 particle with either the vacuum or a different particle. The edge-singularity peaks are contributed by particle excitations of two E8 particles with either the vacuum or another particle, or by particle excitations that contain two sets of two particles with each set including at least a particle of the same type. We also propose a Rydberg qubit array for possible experimental investigation.