Excited-state quantum phase transition and the quantum speed limit

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