Probing quantum phase transitions via quench dynamics in integrable and nearly-integrable systems

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a task challenging for many experimental systems. The measurement of quench dynamics, on the other hand, is a routine practice now in most cold atomic platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in many integrable and near-integrable systems. As a paradigmatic example, we study a global quench in a transverse-field Ising model with nearest- and next-nearest-neighbor interactions. When the model is integrable, we find non-analytic behavior of a dynamical order parameter, which reflects the corresponding ground state quantum phase transition. This behavior persists at finite times in the presence of a weak integrability breaking perturbation. This non-analyticity can be readily observed in experimental platforms such as trapped ions or Rydberg atoms.