Non-equilibrium Renormalization Group Fixed-Points of the Quantum Potts Chain

We devise a renormalization group recursion relation of the Loschmidt amplitude of the quantum Potts chain. The non-equilibrium fixed-points of the renormalization procedure determine the dynamical phases of the system, giving rising to a dynamical quantum phase transition. We will also discuss how there fixed-points affect the dynamical phase transition of the disordered Potts chain and the Loschmidt amplitude of the excited states.