Timescales, dynamical phase transitions and 3rd order phase transitions in the 1d anisotropic XY model

Recent research into time-integrated observables has revealed a special class of states which cap- ture the singular features of the generating functions of those observables, as estimated by full counting statistics (FCS). In this work we extend the results of [Phys. Rev. B 87 184303 (2013)] to the 1d anisotropic XY -model and find a set of FCS critical points associated with the time-integrated transverse magnetization and anisotropy. We show dynamical phase transitions (DPTs) as defined in [Phys. Rev. Lett. 110 135704 (2013)] do not emerge on quenching the states associated with the time-integrated anisotropy across FCS critical points. We also study the timescales required to prepare the associated special states of the transverse magnetization using appropriate Markovian baths and find they are independent of the number of spins in the chain. However the probability to evolve to such a state decreases drastically with increasing system size due to dissipation. Thus when preparing such states it is preferable to use few body systems and to reach the thermodynamic limit it is necessary to use an ancillary system in conjunction with the Markovian baths.