Fisher zeroes and non-analytic real time evolution for quenches in the transverse field Ising model

We study quenches of the magnetic field in the transverse field Ising model. For quenches across the quantum critical point, the boundary partition function in the complex temperature-time-plane shows lines of Fisher zeroes that intersect the time axis, indicating non-analytic real time evolution in the thermodynamic limit (analogous to well-known thermodynamic phase transitions). We obtain exact analytical results for these dynamic transitions and show that the dynamic behavior cannot be obtained from a naive analytic continuation of the thermal equilibrium partition function: Real time evolution across this quantum critical point generates a new non-equilibrium energy scale. We argue that this behavior is expected to be generic for interaction quenches across quantum critical points in other models as well.