Quantum criticality of quantum speed limit for a two-qubit system in the spin chain with the Dzyaloshinsky–Moriya interaction

Abstract

We study the quantum speed limit (QSL) time of a two-qubit system coupled to a spin–chain model with the Dzyaloshinsky–Moriya (DM) interaction. For the Bell state coupled to the Ising model or anisotropic XY model, we find that there is a prominent corresponding relationship between the QSL time and quantum phase transition in a spin–chain environment with larger scale, and the DM interaction can strongly enhance or suppress the response relation. Remarkably, when the surrounding environment is set to the XX model, the DM interaction makes it possible for us to witness the quantum phase transition by the local anomalous enhancement of the QSL time near the critical point. In addition, our analyses indicate that the entanglement can speed-up the system evolution in many-body environment.