Feasibility of the ion-trap simulation of a class of non-equilibrium phase transitions

Our work analyzes the potential of ion traps for the experimental simulation of non-equilibrium phase transitions observed in certain spin-chain models which can be mapped to free-fermion systems. In order to make the dynamics more accessible to an experimenter, we first consider relatively small systems, with few particles. We analyze phase transitions in the non-equilibrium asymptotic regimes of an XY spin chain with a transverse magnetic field and coupled to Markovian baths at the end sites. We study a static open system and a case when the spin chain is periodically kicked. Notably, in the latter case for some anisotropy parameters the dependence on the system size converges rapidly to the many-particle limit, thus facilitating the experimental observation of the dynamics. We also define local observables that indicate the presence of the quantum phase transitions of interest, and we study the effects of the long-range character of the typical interactions obtained in ion traps.