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Journal of Statistical Mechanics Theory and Experiment

Spin echo and geometric phase of a central spin coupled to a compass spin-chain

Wei Wu, Da-Wei Luo, Xu Jingbo

Published Jan 21, 2015• 3 citations
Publisher

Abstract

We investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its statistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin's orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behavior in the vicinity of a quantum phase transition.

DOI
10.1088/1742-5468/2015/01/p01025

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We investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its statistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin's orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behavior in the vicinity of a quantum phase transition.
We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general XYXYXY spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter $\ensuremath{\lambda}$ in spin chain diverges along the critical line $\ensuremath{\lambda}=1$, which suggests an alternative measurement of the quantum criticality of the spin chain.
We study the decoherence process of an exact solvable model that consists of a central spin-1/2 coupling to the surrounding anisotropy spin-1/2 chain in transverse fields. The Loschmidt echo is calculated to study the character of decoherence with different degree of anisotropy. Our results show that the degree of anisotropy γ greatly affects the decoherence process of the central spin-system when the spin chain is in weak transverse fields, but it gives weak effect in the strong transverse field. The decoherence process of the central system changed dramatically along the line of the critical points, and this may be explained as the reflection of quantum phase transitions.
We revisit the problem of decoherence of a qubit centrally coupled to an interacting spin environment, here modeled by a quantum compass chain or an extended XY model in a staggered magnetic field. These two models both support distinct spin-liquid phases, adding a new element to the problem. By analyzing their Loschmidt echoes when perturbed by the qubit we find that a fast decoherence of the qubit is conditioned on the presence of propagating quasiparticles which couple to it. Differently from expectations based on earlier works on central spin models, our result implies that the closeness of an environment to a quantum phase transition is neither a sufficient nor a necessary condition for an accelerated decoherence rate of a qubit.
By introducing the Dzyaloshinsky-Moriya (DM) interaction, the Loschmidt Echo ( LE ) of a quantum system consisting of a central spin and its surrounding environment characterized by an XY spin chain was investigated analytically and numerically. At the critical points of the magnetic field, the LE presents an obvious decay. The decay amplitude can be tuned by the DM interaction. In some specific intervals the DM interaction can remarkably delay the decay of the LE . On the other hand, the DM interaction can change the effects of the anisotropy parameter on the LE.