Quantum speed limit and topological quantum phase transition in an extended XY model

We explore quantum speed limit time tQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that tQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field. or the anisotropy. of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of tQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the threesite interaction a or its anisotropy d. Additionally, we also investigate tQSL for arbitrary time-evolution state in the whole dynamics process and find that tQSL exhibits a behavior of oscillation at non-critical points. However, tQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points. (C) 2022 Elsevier B.V. All rights reserved.