A relation between entanglement and criticality of spin chains is established. The entanglement we exploit is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-1/2 chain. We analytically evaluate the reduced density matrix, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. We find that the entanglement induced by the spin-chain may reach one, and it can signal very well the critical points of the chain. A physical understanding and experimental realization with trapped ions are presented.PACS numbers: 03.65. Ud, 05.70.Jk Quantum entanglement lies at the heart of the difference between the quantum and classical multi-particle world, and can be treated as a useful resource in various tasks such as cryptography, quantum computation and teleportation [1]. Quantum phase transitions [2] are transitions between quantitatively distinct phases of quantum many-body systems, driven solely by quantum fluctuations. In the past decade, a great effort has been devoted to understand the relations between entanglement and quantum phase transitions [3,4,5,6,7,8,9]. In fact, it is natural to associate the quantum phase transition and entanglement once correlations are behind both of them. By sharing this point of view, one anticipates that entanglement induced by a quantum critical many-body system will furnish a dramatic signature of quantum critical points for the many-body system.On the other hand, we usually think of environment that surrounds quantum system as a source of decoherence. Recently researchers have started to investigate the positive effects [10,11,12,13,14,15,16,17] of environment, for example, environment assisted information processing and environment induced entanglement. These investigations pave a new way to engineer mechanisms of preventing, minimizing or using the impact of environment in quantum information processing. In those works, however, the environment was modelled as a set of independent quantum systems, i.e., correlations among particles in the environment were ignored. An interesting open question is whether the correlation among environmental particles can affect the entanglement induced in a bipartite system that couples to it.In this paper, we show how to exploit entanglement in auxiliary particles induced by a quantum critical manybody system as an essential tool to reveal quantum phenomena in the many-body quantum system. Indeed, quantum phase transitions are accompanied by a qualitative change in the nature of classical correlations, such drastic changes in the properties of ground states are often due to the collectiveness/randomness of interparticle couplings which are possibly reflected in entanglement between systems that couple to it. Here we adopt a spin-chain system described by the one-dimensional spin-1 2 XY model as the many-body system. Another pair of spin-1 2 systems that couple to the spin chain would act as the auxiliary particles. We o...

No abstract