Loschmidt Echo and Berry phase of the quantum system coupled to the XY spin chain: Proximity to quantum phase transition

摘要

We study the Loschmidt echo (LE) of a coupled system consisting of a centralspin and its surrounding environment described by a general XY spin-chainmodel. The quantum dynamics of the LE is shown to be remarkably influenced bythe quantum criticality of the spin chain. In particular, the decaying behaviorof the LE is found to be controlled by the anisotropy parameter of the spinchain. Furthermore, we show that due to the coupling to the spin chain, theground-state Berry phase for the central spin becomes nonanalytical and itsderivative with respect to the magnetic parameter $\lambda$ in spin chaindiverges along the critical line $\lambda=1$, which suggests an alternativemeasurement of the quantum criticality of the spin chain.