Quantum speed limit and a signal of quantum criticality

We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.