Quantum quench dynamics in the transverse field Ising model at nonzero temperatures

The recently discovered dynamical phase transition denotes nonanalytic behavior in the real-time evolution of quantum systems in the thermodynamic limit, and it has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this paper, we extend the analysis to nonzero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at nonzero temperatures still displays features derived from the zero-temperature nonanalyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0. This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free-energy density.