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

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