Abstract
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.
Highlights
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
We find that the QSLT has some strong imprint of the quantum phase transition (QPT) for the XY model, even for a finite-sized environment
With the increasing of the driving time, the size of chain or the anisotropy parameter, the critical characteristic of the QSLT becomes more prominent at QPT critical point
Summary
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. We find that the local anomalous enhancement of the QSLT occurs near the critical point. 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.
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