Excited-state quantum phase transition and the quantum speed limit time

Abstract

We investigate the influence of an excited-state quantum phase transition on the quantum speed limit time of an open quantum system. The system consists of a central qubit coupled to a spin environment modeled by a Lipkin-Meshkov-Glick Hamiltonian. We show that when the coupling between qubit and environment is such that the latter is located at the critical energy of the excitedstate quantum phase transition, the qubit evolution shows a remarkable slowdown, marked by an abrupt peak in the quantum speed limit time. Interestingly, this slowdown at the excited-state quantum phase transition critical point is induced by the singular behavior of the qubit decoherence rate, being independent of the Markovian nature of the environment.