Sensitivity to initial conditions on dynamical quantum phase transitions

The dynamical properties of a many-body quantum system are studied in terms of its initial conditions and control parameters in the framework of the Lipkin–Meshkov–Glick model through a quantum quench process. The initial collective pseudospin is considered to lie on the equator of the Bloch sphere and the dynamical phase diagrams are constructed for various values of the polar angle. The two types of dynamical quantum phase transitions (DQPTs) are studied in detail: DQPTs-I, which manifest as non-analyticities of an order parameter as a function of the control parameter; and DQPTs-II, which occur when the rate function of the Loschmidt echo has non-analytical behavior at critical times. By considering relevant domains of the anisotropic parameters of the spin interactions and many examples of initial states, the influence of the initial conditions on both types of DQPTs is examined. The results are presented with emphasis put on the interacting parameters and the initial preparation of the system for their application on experimental settings.