Dynamical Quantum Phase Transitions of Quantum Spin Chains with the Loschmidt-rate Critical Exponent equal to $\frac{1}{2}$

We describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$ . The non-equilibrium renormalization group fixed-point controlling this universality class is described. An asymptotically exact renormalization group recursion relation is derived around this fixed-point to obtain the critical exponent.